Re: yet another question on Mathematica numerical, how to force it to use single precision?


"Nasser Abbasi" <nma@xxxxxxxxx> wrote in message
news:l2lUk.8540$YU2.2535@xxxxxxxxxxxxxxxxxxxxxxx
How can I make Mathemtica give me the same digits to this little sum below
as I get from Fortran or Matlab?
I tried using just N[], which is should use machine precision. I want to
tell it to do the computation in "single precision", i.e. 32 bit as
compared to double precision.

Could some one remind me how to do this?

This is the Mathematica code

---------------------
In[95]:= s = Sum[N[1/k^2], {k, 1, 20000}]
Precision[s]
Accuracy[s]

Out[95]= 1.644884068098209
Out[96]= MachinePrecision
Out[97]= 15.738454476026273
----------------------

This is what I get from Fortran

PROGRAM main
IMPLICIT NONE
REAL :: s
INTEGER :: n,MAX

s = 0.0;
MAX = 20000;

DO n = 1,MAX
s = s + (1./n**2);
END DO

WRITE(*,*), 'sum', s
END PROGRAM main

$ f77 sum_problem.f
$ ./a.exe
sum 1.64472532

------------------------------

This is what I ge from Matlab (by forcing matlab to use single precision

format long g;
s=single(0);
MAX = 20000;
for i=1:MAX
s=s+(1/i^2);
end
s

s =
1.644725

So, Fortran and Matlab generate the same first 6 digits beyond the decimal
point. I want Mathematica to generate those same digits.

Any ideas?



I just tried something.

I think the result of Mathematica is simply the same result as double
precision. So, my question is really, how to make Mathematica use single
precision instead of double precision? When I change Fortran to double it
now gives same digits as Mathematica with N[] or N[,16]

PROGRAM main
IMPLICIT NONE
DOUBLE PRECISION :: s <---- change to double
INTEGER :: n,MAX

s = 0.0;
MAX = 20000;
DO n = 1,MAX
s = s + (1./n**2);
END DO

WRITE(*,1) s
1 format('sum = ', F16.14)
END PROGRAM main

$ ./a.exe
sum = 1.64488406809821

compare to Mathematica with just N[]

Out[95]= 1.644884068098209

But when I use N[,7] in Mathematica hoping to get some number close to what
I get with single precision which is 1.644725, but I still do not

In[122]:= s = Sum[N[1/k^2, 7], {k, 1, 20000}]
1.6448840680982050618`7.000000000000145

Is it possible to do computation in single precision in Mathematica?

Nasser


.

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