IEEE Math Rounding Differs in Compiled .EXE and QB.EXE Editor (26007)

SUMMARY

The results of floating-point calculations may differ between the QuickBasic Version 4.00, 4.00b, or 4.50 QB.EXE editor and an .EXE program compiled with BC.EXE. The BC.EXE compiler produces .EXE programs that return more accurate answers than the QB.EXE editor.

The different answers are caused by rounding differences and the different way in which the intermediate single-precision arithmetic results are stored in the editor versus a compiled .EXE program. Inside the QB.EXE Version 4.00, 4.00b, or 4.50 editor, an 8-byte temporary single-precision floating-point variable is used by default, whereas BC.EXE uses a 10-byte temporary single-precision variable. This information also applies to BC.EXE and QB.EXE in Microsoft Basic Compiler Versions 6.00 and 6.00b for MS-DOS and MS OS/2.

You can force the QB.EXE editor to use a more accurate, 10-byte temporary variable by changing your variables to double precision (DEFDBL A-Z). Note that minor rounding differences may still occur in QB.EXE compared to a compiled .EXE program even when using double precision.

MORE INFORMATION

Example 1

The program in Code Example 1 shown further below should display a value of 2500. Running this program gives the following results using QuickBasic Versions 3.00 and 4.00, 4.00b, or 4.50, comparing single and double precision with and without a coprocessor, and with and without using double precision variables:

QB.EXE 3.00    -- no coprocessor -- (single)  -- 2403.3181     (MBF)
QB.EXE 3.00    -- no coprocessor -- DEFDBL A  -- 2499.xxxx     (MBF)
QB.EXE 4.00    -- no coprocessor -- (single)  -- 2477.24414063 (IEEE) *!
QB.EXE 4.00    -- no coprocessor -- DEFDBL A  -- 2500.0000     (IEEE)
 
QB87.EXE 3.00  -- with coprocessor -- (single) -- 2500.0000  (IEEE)
QB87.EXE 3.00  -- with coprocessor -- DEFDBL A -- 2500.0000  (IEEE)
QB.EXE 4.00    -- with coprocessor -- (single) -- 2477.24414063 * Note!
QB.EXE 4.00    -- with coprocessor -- DEFDBL A -- 2500.0000  (IEEE)
BC.EXE 4.00    -- with coprocessor -- (single) -- 2500.0000  (IEEE)
BC.EXE 4.00    -- with coprocessor -- DEFDBL A -- 2500.0000  (IEEE)

In the Microsoft Binary Format (MBF) in QB.EXE 3.00, miscalculations are due to expected binary format rounding errors. The IEEE format used in QB87.EXE Version 3.00 and QuickBasic Version 4.00 produces a more accurate answer. However, not using DEFDBL in the QB.EXE Version 4.00 (or 4.00b or 4.50) editor produces a less-accurate answer due to a smaller buffer for intermediate calculations.

The following is Code Example 1:

DEFDBL A   ' Try using with and without DEFDBL A for comparison.
n$ = "####.########"
CLS
PRINT "Calculating, please wait...."
a = 1
starttime = TIMER
FOR i = 1 TO 2499
   a = TAN(ATN(EXP(LOG(SQR(a * a))))) + 1
NEXT i
t = TIMER - starttime
CLS
PRINT "calculation complete:"
PRINT USING n$; a, t
END

Example 2

The rounding results performed in IEEE mathematics performed inside the QB.EXE 4.00, 4.00b, or 4.50 editor may differ from a compiled .EXE program, even for double precision. The numbers are similar, but the IEEE rounding is performed differently.

The following program demonstrates this issue by returning 1.19209E-07 inside the editor and 1.084E-19 when compiled to an .EXE program. These results from Code Example 2 occur in QuickBasic Versions 4.00, 4.00b, 4.50 and in Microsoft Basic Compiler Versions 6.00 and 6.00b for MS-DOS and MS OS/2.

The following is Code Example 2:

' For greater accuracy, add DEFDBL A-Z to program, or use e#.
' However, the .EXE program compiled in BC.EXE will still return more
' accurate results than when the program is run in the QB.EXE editor.
e = 1!
DO WHILE e + 1 > 1
   e = e / 2
LOOP
e = 2 * e
PRINT e
END