This tip sheet assumes that you have some idea how numbers are stored on a computer; that you understand what floating point numbers are. For a brief introductory discussion of these concepts you may want to read "How Precise Are the Numerical Values Stored on Computers", the Programmer's Corner article in the March 1992 issue of the Computing News. This article is available on U-Discover!
The accuracy of a computer may be stated in terms of the smallest significant change that can be made to a number and stored. The ratio of this change to the number itself is defined as the "Relative Accuracy" of the computer and is equivalent to the computer's machine epsilon. Here is a comparison of the accuracy of VS FORTRAN programs and UNIX FORTRAN programs. The "UNIX" designation refers to Strauss.
Machine Precision Machine Epsilon
------- --------- ----------------
-7
UNIX single 1.19 x 10
-16
UNIX double 2.22 x 10
-34
UNIX quadruple 1.92 x 10
-7
UDelVM/MVS single 9.54 x 10
-16
UDelVM/MVS double 2.22 x 10
-33
UDelVM/MVS quadruple 3.08 x 10
From the exponent of "machine epsilon," we see that you get about 7
decimal digits of accuracy on UNIX using single precision variables
as compared to about 6 digits on UDelVM and about 16 digits
using double precision on both systems and finally, 34 digits using
quadruple precision on UNIX compared to about 33 on UDelVM. So,
programs moved over to the UNIX system should obtain about the same
if not slightly more accuracy than on UDelVM. Finally, we consider the maximum and minmum range of numbers on each system.
Machine Precision Smallest/Largest Positive Number
------- --------- --------------------------------
UNIX integer [0,2147483647]
UNIX real*4 [1.175494e-38,3.402823e+38]
UNIX real*8 [2.225074d-308,1.797393d+308]
UNIX real*16 [3.362q-4932,1.20q+4932]
UDelVM/MVS integer [0,2147483647]
UDelVM/MVS real*4 [1.0e-78,1.0e+75]
UDelVM/MVS real*8 [1.0d-78,1.0d+75]
UDelVM/MVS real*16 [1.0q-78,1.0q+75]
Thus, if you have programs on UDelVM which generate data values
of the order of 10e75, you will need to convert such programs
to real*8 on UNIX, to obtain the same range of values.
****************************************************************** * * * Correspondence to VS FORTRAN * * * ****************************************************************** * * * VS FORTRAN UNIX * * ========== ==== * * * * Relative Accuracy * * ================= * * * * sp: 9.54e-7 sp: 1.19e-7 * * dp: 2.22d-16 dp: 2.22d-16 * * qp: 3.08q-33 qp: 1.92q-34 * * * * (No changes required..accuracy on UNIX as * * good as or slightly better than UDelVM) * * * * * * Range of Numbers * * ================= * * * * int: [0,2147483647] int: [0,2147483647] * * sp: [1.0e-78,1.0e+75] sp: [1.175494e-38,3.402823e+38] * * dp: [1.0d-78,1.0d+75] dp: [2.225074d-308,1.797393d+308]* * qp: [1.0q-78,1.0q+75] qp: [3.362q-4932,1.20q+4932] * * * * (Programs on UDelVM that generate values in the * * range of [1.0e-78,1.0e+75] need to be converted * * to double precision on UNIX) * * * ******************************************************************
