KnowledgeBase Archive

An Archive of Early Microsoft KnowledgeBase Articles

View on GitHub

Q67887: "Illegal Function Call," Negative Number to Fractional Power

Article: Q67887
Product(s): See article
Version(s): 1.00a 1.00b | 6.00 6.00b 7.00 7.10
Operating System(s): MACINTOSH | MS-DOS
Keyword(s): ENDUSER | B_QuickBas B_GWBasicI | mspl13_basic
Last Modified: 2-JAN-1991

Raising a negative number to a fractional power gives an "Illegal
function call" in BASIC because the result will be a complex number,
which is not supported in BASIC. (A complex number is of the form
x+y*i where x is the real component and y is the imaginary component;
i is the square root of -1.)

Note: -5^(-Y) is not the same as X^(-Y) when X = -5 because -5^(-Y) is
actually parsed as -(5^(-Y)). In other words, the exponentiation
operator (^) has greater precedence than the subtraction (-) operator.

This information applies to most versions of Microsoft BASIC,
including the following:

1. Microsoft QuickBASIC version 1.00 for the Apple Macintosh.
2. Microsoft BASIC Compiler version 1.00 for the Apple Macintosh.
3. Microsoft BASIC Interpreter versions 1.00, 1.01, 2.00, 2.10, and
   3.00 for the Apple Macintosh.
4. Microsoft QuickBASIC versions 1.00, 1.01, 1.02, 2.00, 2.01, 3.00,
   4.00, 4.00b, 4.50 for MS-DOS.
5. Microsoft BASIC Compiler versions 5.35 and 5.36 for MS-DOS.
6. Microsoft BASIC Compiler versions 6.00 and 6.00b for MS OS/2 and
   MS-DOS.
7. Microsoft BASIC Professional Development System (PDS) versions 7.00
   and 7.10 for MS-DOS and MS OS/2.
8. Microsoft GW-BASIC Interpreter versions 3.20, 3.22, 3.23 for
   MS-DOS.

The first PRINT statement below gives "Illegal function call." Many
programmers will try debugging this code by substituting an actual
constant for X, and the PRINT will seem to give the correct result.
However, upon close examination of the precedence of operators, it
will be apparent that the exponential symbol takes precedence over the
minus sign. The expression 5^(-1/6) is parsed first and then the
negation of this expression is performed. The third PRINT demonstrates
what is actually happening in the first PRINT statement:

X = -5
PRINT X ^ (-1 / 6)       ' generates "Illegal function call"
PRINT -5 ^ (-1 / 6)      ' same as PRINT -(5 ^ (-1 / 6)); no error
PRINT (-5) ^ (-1 / 6)    ' generates "Illegal function call"

To avoid the "Illegal function call" message, raise the absolute value
(ABS) of X to the fractional power. If you do this when X is a
negative number, please remember that you must multiply by i (the
square root of -1) to get the true mathematical result. Because the
square root of -1 cannot be represented in BASIC, you must keep track
of imaginary number results yourself using a flag variable or warning
message, for example:

   X=-5
   PRINT ABS(X) ^ (-1 / 6)
   IF SGN(X) < 0 THEN
      PRINT "Warning: the resulting root is an imaginary number. This"
      PRINT "root should be multiplied by i, the square root of -1."
   END IF

THE INFORMATION PROVIDED IN THE MICROSOFT KNOWLEDGE BASE IS PROVIDED "AS IS" WITHOUT WARRANTY OF ANY KIND. MICROSOFT DISCLAIMS ALL WARRANTIES, EITHER EXPRESS OR IMPLIED, INCLUDING THE WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL MICROSOFT CORPORATION OR ITS SUPPLIERS BE LIABLE FOR ANY DAMAGES WHATSOEVER INCLUDING DIRECT, INDIRECT, INCIDENTAL, CONSEQUENTIAL, LOSS OF BUSINESS PROFITS OR SPECIAL DAMAGES, EVEN IF MICROSOFT CORPORATION OR ITS SUPPLIERS HAVE BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. SOME STATES DO NOT ALLOW THE EXCLUSION OR LIMITATION OF LIABILITY FOR CONSEQUENTIAL OR INCIDENTAL DAMAGES SO THE FOREGOING LIMITATION MAY NOT APPLY.