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From: frank on 23 Nov 2009 21:36
On Sun, 22 Nov 2009 18:57:53 -0600, mecej4 wrote:

[snip denormals]
>> [0,0.5) = 1056964608
>
> which is equal to 126 X 2^23. There are seven bits for the biased
> exponent; 2^7=128, but then your numbers don't include +Inf and NaN.
>
>> [0.5,1) = 8388608
> which is exactly 2^23. The significand takes all possible values, while
> the sign and biased exponent are fixed (because the range is 2^-1 to
> 2^0).

I read up on the model for real data when I last read fortran reference,
but I didn't do anything with it. Does what I'm doing here have anything
to do with the above numbers?

dan(a)dan-desktop:~/source$ gfortran real7.f90 -Wall -Wextra -o out
dan(a)dan-desktop:~/source$ ./out
radix is 2
range is 37
dan(a)dan-desktop:~/source$ cat real7.f90
real x
integer d, e
x = .5
d = radix(x)
e = range(x)
print *, "radix is ", d
print *, "range is ", e

end program

! gfortran real7.f90 -Wall -Wextra -o out
! ./out >text1.txt
dan(a)dan-desktop:~/source$
--
frank

"Guns: yes, they are harmful."
From: Ron Shepard on 24 Nov 2009 00:50
In article <7n0859F3jle00U1(a)mid.individual.net>,
frank <frank(a)example.invalid> wrote:

> I was expecting it to split the difference:
>
> dan(a)dan-desktop:~/source$ gfortran real6.f90 -Wall -Wextra -o out
> dan(a)dan-desktop:~/source$ ./out
> 0.50000000 5.96046448E-08
> dan(a)dan-desktop:~/source$ cat real6.f90
> real x
> x = .5
> print *, x, spacing(x)
> end program

Is that the right value to return for SPACING() for an argument of
0.5? From the specification of the function, I would have thought
it should return the smaller number, 2.98E-08.

I would not expect the average value to be returned, or split the
difference, or anything like that. I would expect the difference to
the nearest number to be returned, which is 2.98E-08, not 5.96E-08.

I can think of several reasons why I might prefer the larger of the
two differences to be returned, not the smaller, but that's not the
way the function is defined.

$.02 -Ron Shepard
From: steve on 24 Nov 2009 01:49
On Nov 23, 9:50 pm, Ron Shepard <ron-shep...(a)NOSPAM.comcast.net>
wrote:
> In article <7n0859F3jle0...(a)mid.individual.net>,
>
>  frank <fr...(a)example.invalid> wrote:
> > I was expecting it to split the difference:
>
> > dan(a)dan-desktop:~/source$ gfortran real6.f90 -Wall -Wextra -o out
> > dan(a)dan-desktop:~/source$ ./out
> >   0.50000000      5.96046448E-08
> > dan(a)dan-desktop:~/source$ cat real6.f90
> > real x
> > x = .5
> > print *, x, spacing(x)
> > end program
>
> Is that the right value to return for SPACING() for an argument of
> 0.5?  From the specification of the function, I would have thought
> it should return the smaller number, 2.98E-08.
>

In F95, spacing(x) = b**(e - p) with the radix b, precision p and e
exponent of x. For x = 0.5 and gfortran's default real kind, one has
b = 2, e = 0, p = 24, which gives 5.96xxxe-08. Note, F2003 has a
different but irrelevant definition of spacing().

--
steve
From: frank on 24 Nov 2009 23:00
On Mon, 23 Nov 2009 22:49:30 -0800, steve wrote:


> In F95, spacing(x) = b**(e - p) with the radix b, precision p and e
> exponent of x. For x = 0.5 and gfortran's default real kind, one has b
> = 2, e = 0, p = 24, which gives 5.96xxxe-08. Note, F2003 has a
> different but irrelevant definition of spacing().

What do you mean with "precision" here?

dan(a)dan-desktop:~/source$ gfortran real8.f90 -Wall -Wextra -o out
dan(a)dan-desktop:~/source$ ./out
for sp :
radix is 2
range is 37
p is 24.000000
for dp :
radix is 2
range is 307
q is 52.999999854364731
dan(a)dan-desktop:~/source$ cat real8.f90
implicit integer(a-t)

INTEGER, PARAMETER :: SP=SELECTED_REAL_KIND(6,37)
INTEGER, PARAMETER :: DP=SELECTED_REAL_KIND(15,307)

REAL(KIND=SP) :: x, p
REAL(KIND=DP) :: y, q
x = .5_sp
y = .5_dp
e = 0
d = radix(x)
f = range(x)

print *, " for sp :"
print *, "radix is ", d
print *, "range is ", f

p = e - log(spacing(x))/(log(real(d)))
print *, "p is ", p

print *, " for dp :"
g = radix(y)
h = range(y)
print *, "radix is ", g
print *, "range is ", h

q = e - log(spacing(y))/(log(real(g)))
print *, "q is ", q

end program

! gfortran real8.f90 -Wall -Wextra -o out
dan(a)dan-desktop:~/source$

It looks like precision is 53 for dp on my machine.

--
frank

"Guns: yes, they are harmful."
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