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Microsoft Excel 2007 Bug

Mikko Heinonen 7.2.2008. Microsoft Excel 2007 Bug. Contents. 65535 = 100000 Location of the bug IEEE 754 floating-point format The Bug The Microsoft Hotfix Damages. 65535 = 100000?. Found 22.9.2007 850 * 77,1 = 100000. Should be 65535 Twelve values Excel 2007 formats wrong

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Microsoft Excel 2007 Bug

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  1. Mikko Heinonen 7.2.2008 Microsoft Excel 2007 Bug

  2. Contents • 65535 = 100000 • Location of the bug • IEEE 754 floating-point format • The Bug • The Microsoft Hotfix • Damages

  3. 65535 = 100000? • Found 22.9.2007 • 850 * 77,1 = 100000. Should be 65535 • Twelve values Excel 2007 formats wrong • 9.2*10^18 possible 64-bit floating-point values • ~65535 = 100000 and ~65536 = 100001

  4. Location of the bug • Error in the 64-bit floating-point to string conversion routine. • Routine converts the binary representation of a 64-bit IEEE 754 double to a Unicode text string. • Older 16-bit formatting routine was updated to 32-bit version in Excel 2007.

  5. IEEE 754 64-bit floating-point format • 1 bit for the sign, 11 bits for the exponent, and 52 bits for the mantissa • Mantissa corresponds to 15 digits of decimal accuracy. Excel rounds answers to 15 digits. • 0.1 = 0.000110011001100… • 65535-2^(-37) should be rounded to 65535, but the new 32-bit routine fails.

  6. The Bug • Rendering bug, not a math bug. Numbers stored correctly. 850 * 77,1 * 2 = 131070 • Routine divisor table pointer is pointing to the wrong divisor due to the bug. • 65536(-2^(-37))/65535 = 1, with remainder 1. 1/10000 = 0. 1/1000 = 0. 1 / 100 = 0. 1/10 = 0. 1/1 = 1. => 100001 • -2^(-37) causes the table being misaligned.

  7. The Bug • Overflow possible only when the value sufficiently near an integer 65535. • Routine is hand coded assebly. Likely done to improve performance. • Microsoft engineers should have catch the bug in tests. 65535 = 2^16

  8. The Microsoft Hotfix • Released on 10.10.2007. • 18 days after being found. • Routine fixed by adding new check. • Avoids the overflow causing the table pointer to be set wrong.

  9. Damages • No damages reported. • No security holes found. • Malformed Excel files can be use to find holes or exploits.

  10. References • Chris Lomont : An Analysis of the Excel 2007 “65535” Bug • http://en.wikipedia.org/wiki/IEEE_floating-point_standard

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