Intrinsic functions

Intrinsic functions present a set of the most fundamental functions which are built into the compiler and are directly accessible in your program. These include basic mathematical functions complemented with functions for conversions between different numerical data types. Look at the table below to learn about the most useful functions which you can directly use in your codes.

function	description
SQRT(x)	calculates the square root of x
LOG(x)	calculates the natural logarithm of x (base $e$)
LOG10(x)	calculates the common log of x (base 10)
EXP(x)	raises base $e$ to the x power ($e^x$)
SIN(x)	calculates the sine of x (x expressed in radians)
COS(x)	calculates the cosine of x (x expressed in radians)
TAN(x)	calculates the tangent of x (x expressed in radians)
ASIN(x)	calculates the inverse sine of x (x expressed in radians)
ACOS(x)	calculates the inverse cosine of x (x expressed in radians)
ATAN(x)	calculates the inverse tangent of x (x expressed in radians)
REAL(x)	converts the argument to a real value
INT(x)	converts the argument to an integer value
NINT(x)	rounds x to the nearest integer value
ABS(x)	calculates the absolute value of x
MAX(x1,x2,...)	returns the maximum value of x1, x2, ...

Problem: The normal (Gaussian) distribution function $\phi$ is defined as

$$\phi(x) = \frac{1}{\sqrt{2\pi}} e^{-x^2/2}$$

Write an algorithm to evaluate $\phi(x)$ for values of $x$ from -3.0 to +3.0 in steps of 0.2 and store them in array phi. Display the results.

Solution:

      real phi(50), x, pi
      parameter( pi=3.1415927 )

      x = -3.0
      do while (x .le. 3.0)
         phi(idx) = 1.0/SQRT(2*pi) * EXP(-x**2/2.0)
         write(*,'("For x = ",F4.1,", phi(x) = ",F6.4)') 
     +        x, phi(idx)

         x = x + 0.2
      enddo

When dividing two integers or a real number and an integer, be careful to enter all integers as real numbers. For example, the expression 1/4 is not 0.25, as expected, but zero. When dividing an integer by another integer, F77 automatically rounds the result towards zero. To avoid this, you have to always enter the values in their real expressions. Hence, 1.0/4.0 correctly returns 0.25.

A slightly different case is a division of two variables of type integer or byte. Suppose that we calculate an average of n integral numbers whose sum is stored in variable sum. The average should then be calculated as aver = REAL(sum)/REAL(n). Remember that aver = sum/REAL(n) would give the correct average if sum were of type real.