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[Anonymous]

Hello again,

When trying out some elementary things with real variables in FTN95, I defined 3 real variables x, y and z, of REAL KIND=1, 2 and 3, respectively.
REAL (KIND=1) :: x
REAL (KIND=2) :: y
REAL (KIND=3) :: z

However I got 3 compiler warnings saying:

Specifying the kind of the type REAL with the constant '1' is non-portable - 'SELECTED_REAL_KIND(6,37)' would be better
Specifying the kind of the type REAL with the constant '2' is non-portable - 'SELECTED_REAL_KIND(15,307)' would be better
Specifying the kind of the type REAL with the constant '3' is non-portable - 'SELECTED_REAL_KIND(18,4931)' would be better

A little surprised by these "strange" numbers, I started to play around a bit with log10's and log2's to find out about the internal representation of real variables in FTN95.

KIND=1
---------
To cover a RANGE from -10^37 to 10^37 we need exactly 8 bits for the exponent (7 databits + 1 signbit).
To get a PRECISION of 6 decimal digits we need at least 21 bits (20+1) and maximally 24 bits (23+1) for the mantissa.
So, I guess that a REAL (KIND=1) is represented in 4 bytes with a (24,-division between mantisse and exponent.
In other words: the classical REAL*4.
So far, so good.

KIND=2
---------
To cover a RANGE from -10^307 to 10^307 we need exactly 11 bits for the exponent (10 databits + 1 signbit).
To get a PRECISION of 15 decimal digits we need at least 51 bits (50+1) and maximally 54 bits (53+1) for the mantissa.
So, I guess that a REAL (KIND=2) is represented in 8 bytes with a (53,11)-division between mantissa and exponent.
A rather unexpected division (53,11), but at least we still have the 8-byte representation.
Or is it rather a (52,12)-division?
However, with 12 bits for the exponent we could cover the range -10^616 to 10^616.


But now!

KIND=3
---------
To cover a RANGE from -10^4931 to 10^4931 we need exactly 15 bits for the exponent (14 databits + 1 signbit).
To get a PRECISION of 18 decimal digits we need at least 61 bits (60+1) and maximally 64 bits (63+1) for the mantisse.
If we assume that the PRECISION and RANGE values as supplied by the compiler are correct, that would imply that a REAL (KIND=3) variabale is represented internally by 76 to 79 bits.
Since this interval doesn't contain a multiple of 8 I suppose that a REAL (KIND=3) is represented in 10 bytes (REAL*10) with a (64,16)-division between mantissa and exponent.
However, with 16 bits for the exponent we could cover the range -10^9864 to 10^9864.

I know this is a rather long post, but could anyone confirm the numbers above and the reasoning I have applied?
Maybe I'm a bit old-fashioned, but I like to know how numbers (and objects in general) are represented internally.
I guess this is still a result of my assembler adventures in a previous life...

Many thanks for the feedback and the trouble of checking all this!
Kind regards,
Lucas.

[PaulLaidler]

Lucas

Have you look at the help file under "Kind parameters for intrinsics types" and "Real KINDs".
Also the TRANSFER intrinsic may allow you to look at the bit patterns for given REAL(3) values.