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Q26007: IEEE Math Rounding Differs in Compiled .EXE and QB.EXE Editor

Article: Q26007
Product(s): See article
Version(s): 4.00 4.00b 4.50
Operating System(s): MS-DOS
Keyword(s): ENDUSER | TAR68500 B_BasicCom | mspl13_basic
Last Modified: 17-NOV-1989

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.

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

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