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Ingy döt Net 2023-07-01 11:58:00 -04:00
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Task/Test-integerness/Fortran/test-integerness-1.f Normal file
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MODULE ZERMELO !Approach the foundations of mathematics.
CONTAINS
LOGICAL FUNCTION ISINTEGRAL(X) !A whole number?
REAL*8 X !Alas, this is not really a REAL number.
INTEGER*8 N !Largest available.
IF (ISNAN(X)) THEN !Avoid some sillyness.
ISINTEGRAL = .FALSE. !And possible error messages.
ELSE !But now it is safe to try.
N = KIDINT(X) !This one truncates.
ISINTEGRAL = N .EQ. X !Any difference?
END IF !A floating-point number may overflow an integer.
END FUNCTION ISINTEGRAL !And even if integral, it will not seem so.
LOGICAL FUNCTION ISINTEGRALZ(Z) !For complex numbers, two tests.
DOUBLE COMPLEX Z !Still not really REAL, though.
ISINTEGRALZ = ISINTEGRAL(DBLE(Z)) .AND. ISINTEGRAL(DIMAG(Z)) !Separate the parts.
END FUNCTION ISINTEGRALZ!No INTEGER COMPLEX type is offered.
END MODULE ZERMELO !Much more mathematics lie elsewhere.
PROGRAM TEST
USE ZERMELO
DOUBLE COMPLEX Z
WRITE (6,*) "See if some numbers are integral..."
WRITE (6,*) ISINTEGRAL(666D0),666D0
Z = DCMPLX(-3D0,4*ATAN(1D0))
WRITE (6,*) ISINTEGRALZ(Z),Z
END

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X = 1
10 X = X*BASE
Y = X + 1
D = Y - X
IF (D .EQ. 1) GO TO 10

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MODULE ZERMELO !Approach the foundations of mathematics.
INTERFACE ISINTEGRAL !And obscure them with computerese.
MODULE PROCEDURE ISINTEGRALF4, ISINTEGRALF8,
1 ISINTEGRALZ8, ISINTEGRALZ16
END INTERFACE !Selection is by parameter type and number.
CONTAINS !Sop, now for a grabbag of routines.
LOGICAL FUNCTION ISINTEGRALF8(X) !A whole number?
REAL*8 X !Alas, this is not really a REAL number.
INTEGER*8 N !Largest available.
INTEGER*8 BIG !The first number too big to have any fractional digits in floating-point.
PARAMETER (BIG = RADIX(X)**(DIGITS(X) - 1)) !These "functions" are in fact constants.
IF (ISNAN(X)) THEN !Avoid some sillyness.
ISINTEGRALF8 = .FALSE. !And possible error messages.
ELSE IF (ABS(X).GE.BIG) THEN !But now it is safe to try.
ISINTEGRALF8 = .TRUE. !Can't have fractional digits => integral.
ELSE !But smaller numbers can have fractional digits.
N = KIDINT(X) !So, truncate to an integral value.
ISINTEGRALF8 = N .EQ. X !Any difference?
END IF !So much for inspection.
END FUNCTION ISINTEGRALF8 !No need to look at digit sequences.
LOGICAL FUNCTION ISINTEGRALF4(X) !A whole number?
REAL*4 X !Alas, this is not really a REAL number.
INTEGER*4 N !Largest available.
IF (ISNAN(X)) THEN !Avoid some sillyness.
ISINTEGRALF4 = .FALSE. !And possible error messages.
ELSE IF (ABS(X) .GE. RADIX(X)**(DIGITS(X) - 1)) THEN !Constant results as appropriate for X.
ISINTEGRALF4 = .TRUE. !Can't have fractional digits => integral.
ELSE !But smaller numbers can have fractional digits.
N = INT(X) !So, truncate to an integral value.
ISINTEGRALF4 = N .EQ. X !Any difference?
END IF !A real*4 should not overflow INTEGER*4.
END FUNCTION ISINTEGRALF4 !Thanks to the size check.
LOGICAL FUNCTION ISINTEGRALZ8(Z) !For complex numbers, two tests.
COMPLEX Z !Still not really REAL, though.
ISINTEGRALZ8 = ISINTEGRAL(REAL(Z)) .AND. ISINTEGRAL(AIMAG(Z)) !Separate the parts.
END FUNCTION ISINTEGRALZ8 !No INTEGER COMPLEX type is offered.
LOGICAL FUNCTION ISINTEGRALZ16(Z) !And there are two sorts of complex numbers.
DOUBLE COMPLEX Z !Still not really REAL.
ISINTEGRALZ16 = ISINTEGRAL(DBLE(Z)) .AND. ISINTEGRAL(DIMAG(Z)) !Separate the parts.
END FUNCTION ISINTEGRALZ16 !No INTEGER COMPLEX type is offered.
END MODULE ZERMELO !Much more mathematics lie elsewhere.
PROGRAM TEST
USE ZERMELO
DOUBLE COMPLEX Z
DOUBLE PRECISION X
REAL U
Cast forth some pearls.
WRITE (6,1) 4,DIGITS(U),RADIX(U)
WRITE (6,1) 8,DIGITS(X),RADIX(X)
1 FORMAT ("REAL*",I1,":",I3," digits, in base",I2)
WRITE (6,*) "See if some numbers are integral..."
WRITE (6,*) ISINTEGRAL(666D0),666D0
WRITE (6,*) ISINTEGRAL(665.9),665.9
Z = DCMPLX(-3D0,4*ATAN(1D0))
WRITE (6,*) ISINTEGRAL(Z),Z
END