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# floating point error divide by zero fortran Paluxy, Texas

This page has been accessed 36,212 times. For example, 0/0 (invalid), the system sets the "invalid operation" flag. 6.2.4 Trapping a Floating-Point Exception f95 differs significantly from the earlier f77 compiler in the way it handles floating-point exceptions. For example, the code: integer i,j,k i = 1 j = 0 k = i/j will generate the error "Arithmetic Exception: Integer divide by 0" because an attempt to divide by The first alternative formula is suitable when "b" is positive, the other when it's negative.

For example: REAL*8:: X ! When compiling different routines in a program separately, you should use the same value of n in -fpen. B . . > +Max Representable Value Because each floating-point number type is composed of a finite number of bytes, we can only represent numbers within a given range (see table Sometimes you may notice strings like INF and NaN in fields where only numbers should be; these indicate certain kinds of floating-point exceptions (FPEs).

With certain methods of trapping, you can even provide a subroutine or function that changes the behavior of the floating-point arithmetic, though you should consult a numerical analyst about the consequences See the Fortran User's Guide. For example, the code below would result in a bus error because array 'foo' is declared as real, and array 'dummy' is declared as double precision. When compiling different routines in a program separately, you should use the same value of n in -fpen or /fpe:n.

Error trapping An alternative and reliable method is called "trapping." By trapping, we mean setting a trap at your program's runtime that gets tripped when an FPE occurs, after which the In numerical programs, there are many potential sources for computational error: The computational model could be wrong The algorithm used could be numerically unstable The data could be ill-conditioned The hardware Only really useful for debugging the GNU Fortran compiler itself. -fdump-fortran-optimizedOutput the parse tree after front-end optimization. invalid, overflow, and division C exceptions C C Note: all and common only make sense with set or clear.

Most of the time the formula (x + y)/2 is quite adequate, the FUNCTION above is needed essentially to avoid overflow, so the following scheme may be used: call reset_overflow_flag result IEEE arithmetic allows you to make distinctions about what kind of wrong answers can be ignored, such as NaN or Inf. The IEEE standard for arithmetic specifies a way of handling underflowed results gradually by dynamically adjusting the radix point of the significand. This is done for you in GEOS-Chem file linux_err.c.

Comments The documentation is hard to follow. Floating-Point Computation Prentice-Hall, 1974 ISBN 0-13-322495-3 An old classic presented in a mathematical rigorous way (oouch!): Donald E. See fpversion(1), the Fortran User's Guide, and the Numerical Computation Guide for details. 6.3.1 Flags and ieee_flags() The ieee_flags function is used to query and clear exception status flags. IEEE overflow condition (Overflow Raised) res_oflow = big * big write(6,100)"Overflow: ", big, " *", big, " = ", res_oflow !

The assumption was that trapping would degrade performance while most exceptions were insignificant as long as expected values are returned. For example, the exceptional values +Inf, -Inf, and NaN are introduced intuitively: big*big = +Inf Positive infinity big*(-big) = -Inf Negative infinity num/0.0 = +Inf Where num > 0.0 num/0.0 = The first is sorting the numbers and adding them in ascending order. The standard UNIX name for signal: floating-point exception is SIGFPE.

The recommended method is sorting and adding. Documentation man signal, man fsigctl OS and compiler: UNICOS 10.0.0.3 and f90 Version 3.1.0.0 Compilation f90 job.f job.f explanation Use routines fsigctl, sigoff, and sigon to trap floating-point exceptions and other REAL*16 takes more CPU time than REAL*8/REAL*4, but introduces very small roundoff errors, and has a huge range. The IEEE standard supports user handling of exceptions, rounding, and precision.

This option sets -IPF_fp_speculationstrict (Linux and Mac OS) or /QIPF_fp_speculationstrict (Windows) if no specific -IPF_fp_speculation or /QIPF_fp_speculation option is specified. Choice of algorithms is another critical issue. For instance, prior to the IEEE standard, if you multiplied two very small numbers on a computer, you could get zero. A simple test is as follows: REAL*8:: A A = 0d0 IF ( ABS( A ) > 0d0 ) THEN PRINT*, 'A is not 0 but is ', A ELSE PRINT*,

NOTE: The alternate value that you substitute depends on the type of computation that you are doing...there is no "one-size-fits-all" substitute value. The -fpe or /fpe option enables exceptions in the Fortran main program only. inx = and(rshift(flgs, fp_inexact) , 1) ! For maximum numerically safe performance, perform the key computations in extended precision arithmetic.

In older arithmetic models, the first class of questions might not have the expected answers, while the exceptional cases in the second class might all have the same result: the program IEEE arithmetic offers users greater control over computation than does any other kind of floating-point arithmetic. Not a member? If a floating-point underflow occurs, the result is set to zero and execution continues.

If the optimization level is -O2 or -O3, abrupt underflow to zero is set by default. Floating-point overflow, floating-point divide-by-zero, and floating-point invalid produce exceptional values (NaN and signed Infinities) and execution continues. NOTES: !****************************************************************************** ! ! Trap REAL*4 infinity values IF ( VALUE == Z'7F800000' .or. & VALUE == Z'FF800000' ) THEN IT_IS_A_FINITE = .FALSE.

demo% f95 -g myprog.F demo% dbx a.out Reading symbolic information for a.out ... (dbx) catch FPE (dbx) run Running: a.out (process id 19793) signal FPE (floating point overflow) in MAIN at Setting FTZ on means that denormal results from floating-point calculations will be set to the value zero. With a SPARC processor this result is not accomplished in hardware but in software. Comments: None.

Make X artificially large, Y artificially small for demo purposes X = 1.0d+75 Y = 1.0d-250 ! Target value IF ( ABS( X - VALUE ) < EPSILON ) THEN PRINT*, 'X is within +/- EPSILON of 20.' ELSE PRINT*, 'X is not within +/- EPSILON of 20.' Possible parameter values are shown in the following table TABLE 6-1 ieee_flags ( action, mode, in, out ) Argument Values Argument Values Allowed action get, set, clear, clearall mode direction, exception When the SIGFPE is detected, control passes to the myhandler function, which immediately aborts.

The /fpe:1 option sets -ftz or /Qftz. When disabled, the program is considered to be running with nonstandard arithmetic. However, no vendor has implemented it, to our knowledge. SGI provides utilities ssrun and prof which may be used together to determine where floating-point exceptions occur in your code.

Testing for values close to a non-zero number The procedure for testing if values lie within a specfied tolerance of a non-zero number is similar to the above example, just that FTZ and DAZ are not supported on all IA-32 architectures. sip is a record that has the structure siginfo. This course is referred to as "handling" the error, where the handling you choose may cause the program to abort, print a diagnostic message, or provide a traceback.

and that of b is 1. It seems this method is not used. Arrays in Fortran must have integer subscripts whose values are between 1 and the dimension of the array the subscript refers to.