The minimum and maximum floating point exponent of a real number

Question

How can I get the minimum and maximum exponent for 32- and 64-bit real numbers? I am doing some work to avoid underflows and overflows and would need to know those numbers.

I would also need the base for floating point numbers.

Is it possible in fortran to get the equivalent of ilmach ?

Answer 1

The function range() returns the range of exponents. The intrinsic function huge() returns the maximum allowable number for a given numeric kind. From that you can see the exponent too by employing a logarithm. See also selected_real_kind() .

The base for gfortran and other normal compilers is 2, but you can test it using radix() . They may be some base 10 kinds in the future.

In the same manual I linked you will find other useful intrinsics like tiny(), precision(), epsilon(), spacing() , you can follow the links in "See also:".

Answer 2

For non-zero reals, the numeric model looks like s*b^e*\\sum_{k=1}^{p}f_k*b^{-k} .

To get the value of the base b use radix() . The minimum and maximum values of the exponent e can be found with exponent combined with tiny and huge .

use, intrinsic :: iso_fortran_env, only : real32, real64

print 1, "real32", RADIX(1._real32), EXPONENT(TINY(1._real32)), EXPONENT(HUGE(1._real32))
print 1, "real64", RADIX(1._real64), EXPONENT(TINY(1._real64)), EXPONENT(HUGE(1._real64))

1 FORMAT (A," has radix ", I0, " with exponent range ", I0, " to ", I0, ".")
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