Fortran Intrinsic Functions

Fortran provides many commonly used functions, called intrinsic functions. To use a Fortran function, one needs to understand the following items:

the name and meaning of the function such as ABS() and SQRT()
the number of arguments
the range of the argument
the types of the arguments
the type of the return value or the function value

For example, function SQRT() accepts a REAL argument whose value must be non-negative and computes and returns the square root of the argument. Therefore, SQRT(25.0) returns the square root of 25.0 and SQRT(-1.0) would cause an error since the argument is negative.

Mathematical functions:

*Function*	*Meaning*	*Arg. Type*	*Return Type*
ABS(x)	absolute value of x	INTEGER	INTEGER
ABS(x)	absolute value of x	REAL	REAL
SQRT(x)	square root of x	REAL	REAL
SIN(x)	sine of x radian	REAL	REAL
COS(x)	cosine of x radian	REAL	REAL
TAN(x)	tangent of x radian	REAL	REAL
ASIN(x)	arc sine of x	REAL	REAL
ACOS(x)	arc cosine of x	REAL	REAL
ATAN(x)	arc tangent of x	REAL	REAL
EXP(x)	exp(x)	REAL	REAL
LOG(x)	natural logarithm of x	REAL	REAL

Note that all trigonometric functions use radian rather than degree for measuring angles. For function ATAN(x), x must be in (-PI/2, PI/2). For ASIN(x) and ACOS(x), x must be in [-1,1].

Conversion functions:

*Function*	*Meaning*	*Arg. Type*	*Return Type*
INT(x)	integer part x	REAL	INTEGER
NINT(x)	nearest integer to x	REAL	INTEGER
FLOOR(x)	greatest integer less than or equal to x	REAL	INTEGER
FRACTION(x)	the fractional part of x	REAL	REAL
REAL(x)	convert x to REAL	INTEGER	REAL

Other functions:

*Function*	*Meaning*	*Arg. Type*	*Return Type*
MAX(x1, x2, ..., xn)	maximum of x1, x2, ... xn	INTEGER	INTEGER
MAX(x1, x2, ..., xn)	maximum of x1, x2, ... xn	REAL	REAL
MIN(x1, x2, ..., xn)	minimum of x1, x2, ... xn	INTEGER	INTEGER
MIN(x1, x2, ..., xn)	minimum of x1, x2, ... xn	REAL	REAL
MOD(x,y)	remainder *x - INT(x/y)y**	INTEGER	INTEGER
MOD(x,y)	remainder *x - INT(x/y)y**	REAL	REAL

Functions in an Expression:

Functions have higher priority than any arithmetic operators.
All arguments of a function can be expressions. These expressions are evaluated first and passed to the function for computing the function value.
The returned function value is treated as a value in the expression.

An Example:

The example below has three initialized variables A, B and C. The result is computed and saved into uninitialized variable R.

REAL     ::  A = 1.0, B = -5.0, C = 6.0
REAL     ::  R

R = (-B + SQRT(B*B - 4.0*A*C))/(2.0*A)

The following uses brackets to indicated the order of evaluation:

(-B + SQRT(B*B - 4.0*A*C))/(2.0*A)
     --> ([-B] + SQRT(B*B - 4.0*A*C))/(2.0*A)
     --> (5.0 + SQRT(B*B - 4.0*A*C))/(2.0*A)
     --> (5.0 + SQRT([B*B] - 4.0*A*C))/(2.0*A)
     --> (5.0 + SQRT(25.0 - 4.0*A*C))/(2.0*A)
     --> (5.0 + SQRT(25.0 - [4.0*A]*C))/(2.0*A)
     --> (5.0 + SQRT(25.0 - 4.0*C))/(2.0*A)
     --> (5.0 + SQRT(25.0 - [4.0*C))/(2.0*A)
     --> (5.0 + SQRT(25.0 - 24.0))/(2.0*A)
     --> (5.0 SQRT([25.0 - 24.0]))/(2.0*A)
     --> (5.0 + SQRT(1.0))/(2.0*A)
     --> (5.0 + 1.0)/(2.0*A)
     --> ([5.0 + 1.0])/(2.0*A)
     --> 6.0/(2.0*A)
     --> 6.0/([2.0*A])
     --> 6.0/2.0
     --> 3.0

Therefore, R receives 3.0.