Microsoft Binary Format

In computing, Microsoft Binary Format (MBF) was a format for floating point numbers used in Microsoft's BASIC language products including MBASIC, GW-BASIC and QuickBasic prior to version 4.00.[1][2][3][4][5][6]

History

In 1975, Bill Gates and Paul Allen were working on Altair BASIC, which they were developing at Harvard University on a PDP-10 running their Altair emulator.[7] One thing still missing was code to handle floating point numbers, needed to support calculations with very big and very small numbers,[7] which would be particularly useful for science and engineering.[8][9] One of the proposed uses of the Altair was as a scientific calculator.[10]

Altair 8800 front panel

At a dinner at Currier House, an undergraduate residential house at Harvard, Gates and Allen complained to their dinner companions about having to write this code.[7] One of them, Monte Davidoff, told them he had written floating point routines before and convinced Gates and Allen that he was capable of writing the Altair BASIC floating point code.[7] At the time there was no standard for floating point numbers, so Davidoff had to come up with his own. He decided 32 bits would allow enough range and precision.[11] When Allen had to demonstrate it to MITS, it was the first time it ran on an actual Altair.[12][13] But it worked and when he entered ‘PRINT 2+2’, Davidoff's adding routine gave the right answer.[7]

The source code for Altair BASIC was thought to have been lost to history, but resurfaced in 2000. It had been sitting behind Gates's former tutor and dean Harry Lewis's file cabinet, who rediscovered it.[14][15] A comment in the source credits Davidoff as the writer of Altair BASIC's math package.[14][15]

Radio Shack Tandy TRS-80 Model I System

Altair BASIC took off and soon most early home computers ran some form of Microsoft BASIC.[16][17] The BASIC port for the 6502 CPU, such as used in the Commodore PET, took up more space due to the lower code density of the 6502. Because of this it would likely not fit in a single ROM chip together with the machine-specific input and output code. Since an extra chip was necessary, extra space was available and this was used in part to extend the floating point format from 32 bit to 40 bit.[18] Not long afterwards the Z80 ports, such as Level II BASIC for the TRS-80 (1978), introduced the 64 bit, double precision format as a separate data type from 32 bit, single precision.[19][20][21] Microsoft used the same floating point formats in their implementation of Fortran[22] and for their macro assembler MASM,[23] although their spreadsheet Multiplan[24][25] and their COBOL implementation used binary coded decimal (BCD) floating point.[26] Even so, for a while MBF became the de facto floating point format on home computers, to the point where people still occasionally encounter legacy files and file formats using it.[27][28][29][30][31][32]

VAX-11/780 minicomputer

As early as in 1976, Intel was starting the development of a floating point coprocessor.[33][34] Intel hoped to be able to sell a chip containing good implementations of all the operations found in the widely varying maths software libraries.[33][35] John Palmer, who managed the project, contacted William Kahan, who suggested that Intel use the floating point of Digital Equipment Corporation's (DEC) VAX. The first VAX, the VAX-11/780 had just come out in late 1977 and its floating point was highly regarded. However, seeking to market their chip to the broadest possible market, Intel wanted the best floating point possible and Kahan went on to draw up specifications. When rumours of Intel's new chip reached its competitors they started a standardization effort, called IEEE 754, to prevent Intel from gaining too much ground. Kahan got Palmer's permission to participate; he was allowed to explain Intel's design decisions and their underlying reasoning, but not anything related to Intel's implementation architecture.[33][34][35][36] VAX's floating point formats differed from MBF only in that it had the sign in the most significant bit.[37][38] It turned out that for double precision numbers, an 8 bit exponent isn't wide enough for some wanted operations, e.g. to store the product of two 32-bit numbers.[1]

Intel 8087 floating point coprocessor

Both, Kahan's proposal and a counter-proposal by DEC therefore used 11 bits, like the time-tested 60 bits floating point format of the CDC 6600 from 1965.[34][36][39] Kahan's proposal also provided for infinities, which are useful when dealing with division-by-zero conditions, not-a-number values, which are useful when dealing with invalid operations, denormal numbers, which help mitigate problems caused by underflow,[36][40][41] and a better balanced exponent bias, which can help avoid overflow and underflow when taking the reciprocal of a number.[42][43] In 1980 the Intel 8087 chip was already released,[44] but DEC remained opposed, to denormal numbers in particular, because of performance concerns and since it would give DEC a competitive advantage to standardise on DEC's format. The next year DEC had a study done in order to demonstrate that gradual underflow was a bad idea, but the study concluded the opposite and DEC gave in. In 1985 the standard was ratified, but it had already become the de facto standard a year earlier, implemented by many manufacturers.[34][36][45]

By the time QuickBASIC 4.00 was released, the IEEE 754 standard had become widely adopted - for example, it was incorporated into Intel's 387 coprocessor and every x86 processor from the 486 on. Visual Basic also uses the IEEE 754 format instead of MBF.

Technical details

MBF numbers consist of an eight bit base-2 exponent with bias 129 (value 0: x=0 (00h); exponents -128..-1: x=1..128 (01h..80h), exponents 0..126: x=129..255 (81h..FFh)), a sign bit (positive mantissa: s=0; negative mantissa: s=1) and a 23,[18] 31[18] or 55 bit fractional part of the significand. The decimal point is located before the assumed bit. The MBF double precision format provides less scale than the IEEE 754 format, and although the format itself provides almost one extra decimal digit of precision, in practice the stored values are less accurate because IEEE calculations use 80-bit intermediate results and MBF doesn't.[1][3][46][47] Unlike IEEE floating point, MBF doesn't support denormal numbers, infinities or NaNs.[48]

MBF single-precision format (32 bits, "6-digit BASIC"):

Exponent Sign Significand
8 bits,
bit 31-24 		1 bit,
bit 23 		23 bits,
bit 22-0
xxxxxxxx s mmmmmmmmmmmmmmmmmmmmmmm

MBF extended-precision format (40 bits, "9?-digit BASIC"):

Exponent Sign Significand
8 bits,
bit 39-32 		1 bit,
bit 31 		31 bits,
bit 30-0
xxxxxxxx s mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm

MBF double-precision format (64 bits):

Exponent Sign Significand
8 bits,
bit 63-56 		1 bit,
bit 55 		55 bits,
bit 54-0
xxxxxxxx s mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm

Examples

32-bit format: 84h, 20h, 00h, 00h
40-bit format: 84h, 20h, 00h, 00h, 00h
32-bit format: 81h, 00h, 00h, 00h
40-bit format: 81h, 00h, 00h, 00h, 00h
32-bit format: 00h, 00h, 00h, 00h (or 00h, xxh, xxh, xxh)
40-bit format: 00h, 00h, 00h, 00h, 00h (or 00h, xxh, xxh, xxh, xxh)
32-bit format: 80h, 00h, 00h, 00h
40-bit format: 80h, 00h, 00h, 00h, 00h
32-bit format: 7Fh, 00h, 00h, 00h
40-bit format: 7Fh, 00h, 00h, 00h, 00h
32-bit format: 80h, 80h, 00h, 00h
40-bit format: 80h, 80h, 00h, 00h, 00h
32-bit format: 80h, 35h, 04h, F3h
40-bit format: 80h, 35h, 04h, F3h, 34h
32-bit format: 81h, 35h, 04h, F3h
40-bit format: 81h, 35h, 04h, F3h, 34h
32-bit format: 80h, 31h, 72h, 18h
40-bit format: 80h, 31h, 72h, 17h, F8h
32-bit format: 81h, 38h, AAh, 3Bh
40-bit format: 81h, 38h, AAh, 3Bh, 29h
32-bit format: 81h, 49h, 0Fh, DBh
40-bit format: 81h, 49h, 0Fh, DAh, A2h
32-bit format: 83h, 49h, 0Fh, DBh
40-bit format: 83h, 49h, 0Fh, DAh, A2h

See also

External links

Notes and references

  1. 1 2 3 "IEEE vs. Microsoft Binary Format; Rounding Issues (Complete)". Microsoft Support. November 21, 2006. Retrieved February 24, 2010.
  2. ↑ https://support.microsoft.com/en-us/kb/42980
  3. 1 2 MASM 5.0 Programmer's Guide, p. 133-134. This reference is widely cited, e.g. here http://stackoverflow.com/questions/2686298/convert-pre-ieee-754-c-floating-point-numbers-to-from-c-sharp or here http://collaboration.cmc.ec.gc.ca/science/rpn/biblio/ddj/Website/articles/CUJ/1990/9008/pugh/pugh.htm - read with care though. The second reference could be mistaken to say that QB 4.0 could use MBF internally, but it only uses IEEE. It just has a few conversion functions to convert IEEE floating point numbers to strings containing MBF data, e.g. MKDMBF$ in addition to MKD$ which just copies the bytes of the IEEE value to a string.
    The MASM 6.1 documentation notes that 5.1 was the last MASM version to support MBF: http://people.sju.edu/~ggrevera/arch/references/MASM61PROGUIDE.pdf
  4. ↑ GW-BASIC User's Manual, Appendix D.3 USR Function Calls
  5. ↑ BASIC Second edition (May 1982), IBM: Appendix C-15 (This is the BASICA manual.)
  6. ↑ http://www.trs-80.com/trs80-zaps-internals.htm#rommath
  7. 1 2 3 4 5 http://news.harvard.edu/gazette/story/2013/09/dawn-of-a-revolution
  8. ↑ http://www.sciencedirect.com/science/article/pii/0898122187901817
  9. ↑ http://cis.poly.edu/~mleung/CS3734/s05/ch01/floatingPoints2.pdf
  10. ↑ https://books.google.nl/books?id=klV_BAAAQBAJ&pg=PA16
  11. ↑ http://altairbasic.org/math_ex.htm
  12. ↑ Triumph of the Nerds
  13. ↑ http://www.theregister.co.uk/2001/05/11/microsoft_altair_basic_legend_talks
  14. 1 2 http://www.theregister.co.uk/2001/05/13/raiders_of_the_lost_altair
  15. 1 2 https://web.archive.org/web/20020102173701/http://www.rjh.org.uk/altair/ian.htm
  16. ↑ http://www.oldcomputers.net/important-computer-people.html
  17. ↑ http://comp.lang.basic.powerbasic.narkive.com/erBpXdwr/basic-7-0-for-windows#post4
  18. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 http://www.pagetable.com/?p=46
  19. ↑ https://archive.org/details/Level_II_BASIC_Reference_Manual_1st_Ed._1978_Radio_Shack
  20. ↑ http://akhara.com/trs-80/docs/model1/Level%20II%20BASIC%20Reference%20Manual%20(1979)(Radio%20Shack)(pdf).zip
  21. ↑ https://ia800902.us.archive.org/17/items/BASIC-80_MBASIC_Reference_Manual/BASIC-80_MBASIC_Reference_Manual_text.pdf
  22. ↑ http://www.textfiles.com/bitsavers/pdf/microsoft/cpm/Microsoft_FORTRAN-80_Ver3.4_Users_Manual_Nov80.pdf (page 45 and 55)
  23. ↑ ftp://ftp.gwdg.de/pub/mpsf/pc_doc/dosbesch.ps (page 89 and 20)
  24. ↑ http://www.classiccmp.org/dunfield/kyocera/t200mpln.pdf (page 27 = 42 in the PDF)
  25. ↑ Microsoft C Pcode Specifications, page 13; Multiplan wasn't compiled to machine code, but to a kind of byte-code which was run by an interpreter, in order to make Multiplan portable across the widely varying hardware of the time. This byte-code distinguished between the machine-specific floating point format to calculate on, and an external (standard) format, which was binary coded decimal (BCD). The PACK and UNPACK instructions converted between the two.
  26. ↑ http://www.textfiles.com/bitsavers/pdf/microsoft/cpm/Microsoft_COBOL-80_1978.pdf (page 26 = 32 in the PDF)
  27. ↑ http://www.textfiles.com/programming/qwk.txt
  28. ↑ http://www.csidata.com/patch/csim.txt
  29. ↑ https://www.7api.com/converting-microsoft-binary-format-to-ieee-format-using-vb-6-beatfx.html
  30. ↑ http://www.tek-tips.com/viewthread.cfm?qid=592713
  31. ↑ https://social.msdn.microsoft.com/Forums/vstudio/en-US/64a201b5-852d-41df-9abe-2ad2645cc937/reading-binary-format-qbasic-with-c?forum=netfxbcl
  32. ↑ http://r.789695.n4.nabble.com/Reading-MetaStock-data-format-in-R-td4677240.html
  33. 1 2 3 http://www.intel.com/content/dam/www/public/us/en/documents/case-studies/floating-point-case-study.pdf
  34. 1 2 3 4 https://www.cs.berkeley.edu/~wkahan/ieee754status/754story.html
  35. 1 2 http://www.drdobbs.com/architecture-and-design/a-conversation-with-william-kahan/184410314
  36. 1 2 3 4 http://www.dr-chuck.com/dr-chuck/papers/columns/r3114.pdf
  37. ↑ http://nssdc.gsfc.nasa.gov/nssdc/formats/VAXFloatingPoint.htm The VAX-11/780 didn't implement the "G" format yet. Although this is not directly apparent from the tables because the structures have been cut up in two-byte words, the byte order is actually the same as on modern CPUs. There isn't enough room in the exponent range for NaNs, infinities or denormals.
  38. ↑ http://www.ece.cmu.edu/~ece447/s15/lib/exe/fetch.php?media=vax_hwhbk_1979.pdf
  39. ↑ http://ygdes.com/CDC/DesignOfAComputer_CDC6600.pdf
  40. ↑ https://www.cs.berkeley.edu/~wkahan/ieee754status/why-ieee.pdf
  41. ↑ https://www.cs.berkeley.edu/~wkahan/JAVAhurt.pdf
  42. ↑ https://books.google.nl/books?id=sUD8CAAAQBAJ&pg=PA171
  43. ↑ https://www.cs.berkeley.edu/~wkahan/ieee754status/Names.pdf
  44. ↑ http://micro.magnet.fsu.edu/optics/olympusmicd/galleries/chips/intel8087.html
  45. ↑ https://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF
  46. ↑ http://community.embarcadero.com/index.php/article/technical-articles/162-programming/14799-converting-between-microsoft-binary-and-ieee-forma Warning: although the explanation of the format is correct, the actual code isn't flawless.
  47. ↑ https://groups.google.com/forum/#!topic/comp.os.msdos.programmer/mDyRI1wolAc Discussion about MBF. The first comment misses the mark, since IEEE floating point didn't exist yet.
  48. ↑ http://www.boyet.com/Articles/MBFSinglePrecision.html
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