Fortran 90 on Digital UNIX
The system parameters on Digital's Alpha-computer, using Digital UNIX
and the Digital Fortran 90 compiler are given here. Compare the corresponding
table for NAG or Cray.
Digital and Cray use the number of bytes as the KIND-parameter.
Digital permits the values 1, 4, 8 and 16 for logical variables
(with the same result as for the default value 4), the values 2,
4 and 8 for integers, the values 4, 8 and 16 for floating point
values, and the values 4 and 8 for complex values. The name quad
for the case KIND=16 is my own! Also the names int15,
int31, and int63 are mine.
LOGICAL Default byte word
KIND number = 4 1 4
LOGICAL Default double quad
KIND number = 4 8 16
INTEGER int15 int31 int63
KIND number = 2 4 8
digits = 15 31 63
radix = 2 2 2
range = 4 9 18
huge = 32767 2147483647 9223372036854775807
bit_size = 16 32 64
REAL single double quad
KIND number = 4 8 16
digits = 24 53 113
maxexponent = 128 1024 16384
minexponent = -125 -1021 -16381
precision = 6 15 33
radix = 2 2 2
range = 37 307 4931
epsilon = 0.11920929E-06 0.22204460E-15 0.19259299E-33
tiny = 0.11754944E-37 0.22250739-307 0.33621031-4931
huge = 0.34028235E+39 0.17976931+309 0.11897315+4933
COMPLEX single double
KIND number = 4 8
precision = 6 15
range = 37 307
I here give the major switches to the compilation command on Digital.
I recommend the command man f90 for further information.
The source code in fix form should have the extension .f, .for
or .FOR, while the source code in free form should
have the extension .f90.
Note especially that using these switches it is possible to choose
different sizes (number of bits) for integers (with integer_size),
single precision values (with real_size) and double precision
numbers (with double_size) to the desired bit-length (number
of bytes). Since the Alpha processor is a 64-bit processor it is
recommended to use 64 bits for the floating point numbers, that
is to use the extension -real_size 64 or simpler -r8.
- The default case is single precision with four bytes and double
precision with eight bytes.
- Please note that the switch -r8 gives that both single
and double precision uses eight bytes. Double precision and single
precision are thus the same in this case!
- The corresponding remark applies to the switch -r16,
in which case both single and double precision have sixteen bytes.
- Using only the switch -double_size 128 gives single
precision with four bytes and double precision with sixteen bytes.
- The hybrid with the switch -double_size 64 -r16 gives
both single precision and double precision with sixteen bytes.
The system thus follows the Fortran standard, which requires that
double precision at least shall have the same accuracy as single
precision.
- If you wish to double both single and double precision you should
use the switch -double_size 128 -r8.
- All calculations with 128 bits (sixteen bytes, quad precision)
are slow! See for example the table at the end of the Solution
9.2 to Exercise 9.2 in chapter 9.
-c Only compilation (no linking)
-C Index check
-double_size 64 (default)
-double_size 128 (double precision becomes quad)
-f fixed The old form of the source code (fix form)
-f free The new form of the source code (free form)
-g Creates debug information
-i Selects the integer length. Use
-i2 or integer_size 16
-i4 or integer_size 32 (default)
-i8 or integer_size 64
-Idir Fortran 90 looks for files for the
Fortran INCLUDE statement in this directory
-l Linking of libraries
-o Naming the final program
-O Optimization
-pg Generates execution profile for gprof
-real_size 32 (default)
-real_size 64 or -r8
-real_size 128 or -r16
-u Implies IMPLICIT NONE without an explicit statement
in each program unit
-v Comments how the compilation proceeds
-V Writes the source code with the extension .l
-version Gives the version number of the compiler
-vms Gives certain VAX VMS properties (does not switch
to VAX-arithmetics)
-w Suppresses warnings
Since DEC Alpha is a 64-bit processor it is especially interesting
to study the various precisions, especially single and quad precision,
and how to switch between the different precisions.
My tests indicate that it follows IEEE 754 correctly (single and
double precision, higher precisions are not yet standardized).
Rounding parameter
The first example is the calculation of the rounding parameter 
in the program EPSILON. This program, which is written in
normal single precision, is in the file epsilon.f90.
It has been run in all the three possible precisions.
% f90 epsilon.f
% a.out
mu = 5.9604645E-08
% f90 -r8 epsilon.f
% a.out
mu = 1.110223024625157E-016
% f90 -r16 epsilon.f
% a.out
mu = 9.629649721936179265279889712924637E-0035
%
Three precisions simultaneously
The second example is summation forwards and backwards, with the
program SUMMATION. This program is in the file sum.f90.
Its mathematical/numerical task is to show that summation starting
with the smallest values gives the most accurate result. At one
run this program handles all three possible precisions.
Single and double precision are specified in the ordinary way
with REAL and DOUBLE PRECISION, respectively,
while for quad precision we use the possibility of introducing a
user-selected precision, which is given the name QUAD.
The definition uses the function SELECTED_REAL_KIND
in order to obtain a suitable (KIND-number), see chapter
13.
% f90 sum.f90
% a.out
How many numbers do you wish to add? 1e6
Do you want to add forwards (F) or backwards (B)? f
Summation forwards of 1000000 numbers.
The sum in single precision = 1.644725
The sum in double precision = 1.64493306684877
The sum in quad precision = 1.64493306684872643630574849997952
% a.out
How many numbers do you wish to add? 1e6
Do you want to add forwards (F) or backwards (B)? b
Summation backwards of 1000000 numbers.
The sum in single precision = 1.644933
The sum in double precision = 1.64493306684873
The sum in quad precision = 1.64493306684872643630574849997939
%
It is easy to switch the double precision to quad precision through
compiling the program sum.f90
with
% f90 -double_size 128 sum.f90
but it is not possible to switch the single precision, since the notation
0.0_QUAD then gives a compilation error. If we replace the
offending expression with 0.0 (and the corresponding substitutions
for any other constants) we can use
% f90 -r8 sum.f90
to obtain that both single and double precision are treated as double
precision, while quad precision remains unaffected. With
% f90 -r16 sum.f90
all calculations are done in the quad precision.
Back to the Digital section in appendix
6.
Latest modification: 9 March 1996
boein@nsc.liu.se | 
