Article ID: 69333  View products that this article applies to. This article was previously published under Q69333 SUMMARY
To reliably test whether two floatingpoint variables or expressions
are equal (using IEEE format or MBF), you must subtract the two
variables being compared and test whether their difference is less
than a value chosen at the limits of significance for single or double
precision. NO OTHER TEST FOR EQUALITY WILL BE RELIABLE. The following
formulas reliably test whether X and Y are equal:
MBF (Microsoft Binary Format) is found in Microsoft QuickBasic for MSDOS (QB.EXE noncoprocessor version only), versions 1.0, 1.01, 2.0, 2.01, and 3.0, and in Microsoft GWBasic Interpreter for MSDOS, versions 3.2, 3.22, and 3.23. The information in this article is also included in the Help file provided with the Standard and Professional Editions of Microsoft Visual Basic for MSDOS, version 1.0. MORE INFORMATION
NOTE: Significant digits in a calculated number can be lost due to
the following: multiple calculations, especially addition of
numbers far apart in value, or subtraction of numbers similar in
value. When a number results from multiple calculations, you may
need to change your test for equality to use fewer significant
digits to reflect the mathematical loss of significant digits. If
your test of significance uses too many significant digits, you may
fail to discover that numbers compared for equality are actually
equal within the possible limit of accuracy.
In the Basic products listed above that use IEEE floatingpoint format, intermediate calculations are performed in an internal 64bit temporary register, which has more bits of accuracy than are stored in singleprecision or doubleprecision variables. This often results in an IF statement returning an error which states that the intermediate calculation is not equal to the expression being compared. For example:
Reference: Both the IEEE and MBF standards attempt to balance accuracy and precision with numeric range and speed. Accuracy measures how many significant bits of precision are not lost in calculations. Precision refers to the number of bits in the mantissa, which determines how many decimal digits can be represented. Both IEEE format and MBF store numbers of the form 1.x to the power of y (where x and y are base 2 numbers; x is the mantissa, and y is the exponent). MBF single precision has 24 bits of mantissa, and double precision has 56 bits of mantissa. All MBF calculations are performed within just 24 or 56 bits. IEEE single precision has 24 bits of mantissa, and double precision has 53 bits of mantissa. However, all singleprecision and doubleprecision IEEE calculations in Visual Basic for MSDOS, version 1.0; in QuickBasic for MSDOS, versions 3.0/4.x; in Basic Compiler for MSDOS, versions 6.0, and 6.0b; and in Basic PDS for MSDOS, versions 7.0 and 7.1re performed in a 64bit temporary register for greater accuracy. As a result, IEEE calculations are more accurate than MBF calculations, despite MBF's ability to represent more bits in double precision. Most numbers in decimal (base 10) notation do NOT have an exact representation in the binary (base 2) floatingpoint storage format used in singleprecision and doubleprecision data types. Both IEEE format and MBF cannot exactly represent (and must round off) all numbers that are not of the form 1.x to the power of y (where x and y are base 2 numbers). The numbers that can be exactly represented are spread out over a very wide range. A high density of representable numbers is near 1.0 and 1.0, but fewer and fewer representable numbers occur as the numbers go towards 0 or infinity. The above limitations often cause Basic to return floatingpoint results different than you might expect. More information on this topic can be found in the Microsoft Knowledge Base by querying on the following words:
floating and point and format and QuickBasic
The IEEE floating point format is documented in the following manuals:
MBF AND conversion AND exponent
PropertiesArticle ID: 69333  Last Review: August 16, 2005  Revision: 2.2 APPLIES TO
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