Mixed Mode Arithmetic Expressions

If operands in an expression contains both INTEGER and REAL constants or variables, this is a mixed mode arithmetic expression.

In mixed mode arithmetic expressions, INTEGER operands are always converted to REAL before carrying out any computations. As a result, the result of a mixed mode expression is of REAL type. The following is a table showing this fact.

Operator	INTEGER	REAL
INTEGER	INTEGER	REAL
REAL	REAL	REAL

The rules for evaluating mixed mode arithmetic expressions are simple:

Use the rules for evaluating single mode arithmetic expressions for scanning.
After locating an operator for evaluation, do the following:

if the operands of this operator are of the same type, compute the result of this operator.
otherwise, one of the operand is an integer while the other is a real number. In this case, convert the integer to a real (i.e., adding .0 at the end of the integer operand) and compute the result. Note that since both operands are real numbers, the result is a real number.

There is an exception, though. In a**n, where a is a real and n is a positive integer, the result is computed by multiplying n copies of a. For example, 3.5**3 is computed as 3.5*3.5*3.5

Simple Examples:

1 + 2.5 is 3.5
1/2.0 is 0.5
2.0/8 is 0.25
-3**2.0 is -9.0
4.0**(1/2) is first converted to 4.0**0 since 1/2 is a single mode expression whose result is 0. Then, 4.0**0 is 1.0

An Important Note:

In expression a**b where a is REAL, the result is undefined if the value of a is negative. For example, -4.0**2 is defined with -16.0 as its result, while (-4.0)**2 is undefined.

More Complicated Examples:

In the following, brackets will be used to indicated the order of evaluation and braces will be used to indicated an integer-to-real conversion.

Note that 6.0 ** 2 is not converted to 6.0 ** 2.0. Instead, it is computed as 6.0 * 6.0.

5 * (11.0 - 5) ** 2 / 4 + 9
     --> 5 * (11.0 - {5}) ** 2 / 4 + 9
     --> 5 * (11.0 - 5.0) ** 2 / 4 + 9
     --> 5 * ([11.0 - 5.0]) ** 2 / 4 + 9
     --> 5 * 6.0 ** 2 / 4 + 9
     --> 5 * [6.0 ** 2] / 4 + 9
     --> 5 * 36.0 / 4 + 9
     --> {5} * 36.0 / 4 + 9
     --> 5.0 * 36.0 / 4 + 9
     --> [5.0 * 36.0] / 4 + 9
     --> 180.0 / 4 + 9
     --> 180.0 / {4} + 9
     --> 180.0 / 4.0 + 9
     --> [180.0 / 4.0] + 9
     --> 45.0 + 9
     --> 45.0 + {9}
     --> 45.0 + 9.0
     --> 54.0

In the following, 25.0 ** 1 is not converted, and 1 / 3 is zero.

25.0 ** 1 / 2 * 3.5 ** (1 / 3)
     --> [25.0 ** 1] / 2 * 3.5 ** (1 / 3)
     --> 25.0 / 2 * 3.5 ** (1 / 3)
     --> 25.0 / {2} * 3.5 ** (1 / 3)
     --> 25.0 / 2.0 * 3.5 ** (1 / 3)
     --> 12.5 * 3.5 ** (1 / 3)
     --> 12.5 * 3.5 ** ([1 / 3])
     --> 12.5 * 3.5 ** 0
     --> 12.5 * [3.5 ** 0]
     --> 12.5 * 1.0
     --> 12.5

Click here to continue with single mode arithmetic expressions.