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Precision query - how to solve KIND=16

 
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arctica



Joined: 10 Sep 2006
Posts: 105
Location: United Kingdom
PostPosted: Tue Dec 05, 2023 3:04 pm    Post subject: Precision query - how to solve KIND=16 Reply with quote
Hello

Is there a way to get the real(kind=16) or a workaround for this in ftn95?

The following code works if real(kind=2) (i.e. double precision):

Code:
program feigenbaum
      implicit none

      integer i, j, k
      real(kind=2) :: x, y, a, a1, a2, d1 ! kind=2 double precision
      !real ( KIND = 16 ) x, y, a, b, a1, a2, d1

      print '(a4,a13)', 'i', 'd'

      a1 = 1.0;
      a2 = 0.0;
      d1 = 3.2;

      do i=2,20
         a = a1 + (a1 - a2) / d1;
         do j=1,10
            x = 0
            y = 0
            do k=1,2**i
                y = 1 - 2 * y * x;
                x = a - x**2;
            end do
            a = a - x / y;
         end do

         d1 = (a1 - a2) / (a - a1);
         a2 = a1;
         a1 = a;
         print '(i4,f13.10)', i, d1
     end do
     end



I cannot reproduce the results below with real(kind=2):

i d
2 3.2185114220
3 4.3856775986
4 4.6009492765
5 4.6551304954
6 4.6661119478
7 4.6685485814
8 4.6690606606
9 4.6691715554
10 4.6691951560
11 4.6692002291
12 4.6692013133
13 4.6692015458
14 4.6692015955
15 4.6692016062
16 4.6692016085
17 4.6692016090
18 4.6692016091
19 4.6692016091
20 4.6692016091

Thanks
Lester
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PaulLaidler
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Joined: 21 Feb 2005
Posts: 8017
Location: Salford, UK
PostPosted: Tue Dec 05, 2023 3:50 pm    Post subject: Reply with quote
REAL(KIND=3) can be used for 32 bit applications.
This gives 80 bit extended precision.
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arctica



Joined: 10 Sep 2006
Posts: 105
Location: United Kingdom
PostPosted: Tue Dec 05, 2023 5:22 pm    Post subject: Re: Reply with quote
Get a bit closer to the published value at iteration 14 using kind=3 and win32 option:

i d
2 3.21851142203808791280
3 4.38567759856833909170
4 4.60094927653807532040
5 4.65513049539197968780
6 4.66611194782857030690
7 4.66854858144686456730
8 4.66906066064807793730
9 4.66917155538151432430
10 4.66919515602275888650
11 4.66920022908290646170
12 4.66920131315636925260
13 4.66920154625723728170
14 4.66920159550432773820
15 4.66920148627286091600
16 4.66920254043202110470
17 4.66919736236123777780
18 4.66920562189315892730
19 4.66896400405368285560
20 4.67168279116043707170

PaulLaidler wrote:
REAL(KIND=3) can be used for 32 bit applications.
This gives 80 bit extended precision.
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PaulLaidler
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Joined: 21 Feb 2005
Posts: 8017
Location: Salford, UK
PostPosted: Tue Dec 05, 2023 5:52 pm    Post subject: Reply with quote
At a quick glance it looks like you may be dividing one very small value by another very small value. If you are then there will be problems with round-off error (no matter what the precision).
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wahorger



Joined: 13 Oct 2014
Posts: 1226
Location: Morrison, CO, USA
PostPosted: Wed Dec 06, 2023 12:56 am    Post subject: Reply with quote
In this line
Code:
y = 1 - 2 * y * x;

the default is 32-bit. Since you wish 80-bit, then define two parameters as
Code:
real (kind=3),parameter:: one=1.0_3,two=2._3

and recode this line as
Code:
y = one - two * y * x;

or
Code:
y = 1.0_3 - 2.0_3 * y * x;


This should help.

[edited]
BTW, it turns out if you put, say, 1.1 as a constant without the _3, the value of the constant will not be 1.1, rather 1.1000000238418579.
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JohnCampbell



Joined: 16 Feb 2006
Posts: 2584
Location: Sydney
PostPosted: Wed Dec 06, 2023 7:28 am    Post subject: Reply with quote
Just a note to "clarify".
If you use a (real*4) constant, such as in (real*8) d1 = 3.2, this will set the extended bits beyond 3.2_1 to zero.
This gives a different value where the extended bits are non zero for the extended precision constant.
The most common occurrence for this is the constant 0.1

Code:
  real*10 x,y,z
!  the following are different
  x = 1.1
  y = 1.1d0
  z = 1.1_3
  write (*,*) x,y,z,'  all different values'

!  the following are the same
  x = 1.0
  y = 1.0_3
  z = 1
  write (*,*) x,y,z,'  all same values'
end


Statements like "X = 2" will not cause any problems as the real*10 value has zero bits in the extended precision bytes. You just have to check what the default kind is during the computation.
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