Numerical Precision in Fortran 95:
fortran, fortran95, gfortran, numerical-analysis
Solution
I do know a bit of Fortran ! @Dougal's answer is correct though the snippet he quotes from is not, embedding the letter `d` into a real literal constant is not required (since Fortran 90), indeed many Fortran programmers now regard that approach as archaic. The snippet is also misleading in advising the use of `3.1415926535d+0` to initialise a 64-bit floating-point value for pi, it doesn't set enough of the digits to their correct values.
The statement:
Real(Kind=8)::Pi1=3.1415926535897932384626433832795028841971693993751058209
defines `Pi1` to be a real variable of kind 8. The literal real value `3.1415926535897932384626433832795028841971693993751058209` is, however, a real value of default kind, most likely to be a 4-byte real on most current compilers. That seems to explain your output but do check your documentation.
On the other hand, the literal real value `Pi2=3.1415926535897932384626433832795028841971693993751058209_8` is, by the suffixing of the kind specification, declared to be of kind=8 which is the same as the kind of the variable it is assigned to.
Three more points:
1) Don't fall into the trap of thinking that `kind=8` means the same thing as `64-bit floating-point number` or `double`. For many compilers it does, for some it doesn't. Kind numbers are not portable between Fortran implementations. They are, according to the standard, arbitrary positive integers. Better, with a modern compiler, would be to use the predefined constants from the intrinsic module `iso_fortran_env`, e.g.
use, intrinsic :: iso_fortran_env
...
real(real64) :: pi = 3.14159265358979323846264338_real64
There are other portable approaches to setting variable kinds using functions such as `selected_real_kind`.
2) Since the value of `pi` is unlikely to change during the execution of your program you might care to make it a parameter thus:
real(real64), parameter :: pi = 3.14159265358979323846264338_real64
3) It isn't necessary (or usual) to end Fortran statements with a ';' unless you want to have more than one statement on the same line in the source file.
Problem
I have the following Fortran code: ``` Program Strange Real(Kind=8)::Pi1=3.1415926535897932384626433832795028841971693993751058209; Real(Kind=8)::Pi2=3.1415926535897932384626433832795028841971693993751058209_8; Print*, "Pi1=", Pi1; Print*, "Pi2=", Pi2; End Program Strange ``` I compile with gfortran, and the output is: ``` Pi1= 3.1415927410125732 Pi2= 3.1415926535897931 ``` Of course the second is correct, but should this be the case? It seems like Pi1 is being input to memory as a single precision number, and then put into a double precision memory slot. But this seems like an error to me. Am I correct?