Fortran 90 on Digital UNIX

• System parameters on Digital UNIX
• Compilation on Digital UNIX
• Some examples on using Digital UNIX

System parameters on Digital UNIX

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

Compilation on Digital UNIX

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

Some examples on using Digital UNIX

My tests indicate that it follows IEEE 754 correctly (single and double precision, higher precisions are not yet standardized).

Rounding parameter

% 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
% 

% f90 -double_size 128 sum.f90

% f90 -r8 sum.f90

% f90 -r16 sum.f90