[Intel] "New" Celeron dictated by marchitecture, not architecture

The Inquirer ^ | July 11, 2002 | Andrew Busigin

[supercat]

Indeed while AMD has stubbornly refused to die, Cyrix, WinChip, Harris, and others are no longer in the X86 CPU business, and indeed many of the original second source companies no longer even exist, except perhaps for some of their intellectual properties and patent licences surviving in other companies like VIA.

I wonder if anyone's using Cyrix's patented method for long division? Shortly after the Pentium F-div fiasco, I found myself thinking there must be a way of accellerating division that wasn't so horrendously complicated; I found it, but unfortunately when I did a patent search someone at Cyrix had beat me to it (their method was slightly different, but quite similar).

Essentially, my method takes advantage of the fact that if the first N bits of the divisor are all "1"'s and the next group of N bits from the divident or partial remainder equals x, then the next N bits of the quotient must be either x or x+1; the determination of which is correct may be deferred until the end, if an extra couple bits are kept for each partial quotient ( Example:

                  123,565,155,653,854,108

                  123,564¹154¹652²852²107 R ¹953,073
999,123 ) 123,456,789,012,345,678,901,234
          122,892,129
              564,660,012
              563,505,372
                1,154,640,345
                1,152,987,942
                    1,652,403,678
                    1,650,551,196
                        1,852,482,901
                        1,850,375,796
                            2,107,105,234
                            2,105,152,161
                                1,953,073

This example was worked base-1000. Note that each partial quotient equals the leading part of its partial remainder (for partial quitients over 1,000, the first digit is shown superscripted). The partial quotients need to be summed, and the excess from the "remainder" needs to be added to the least significant digit of the quotient, but these are comparatively minor steps and may be easily parallelized.

BTW, while most divisors won't be of the form "11111xxxxxx" [binary] or "99999xxxx" [decimal], it's easy to compute an approximate reciprocal which, when multiplied by the divisor, will yield one of appropriate form. Multiplying divisor and dividend by the same value will not change the quotient.

[HAL9000]

Whether this was because the early graphics board designs were for big-endian computers, or whether it was because it made the graphics look like their conventionally-printed binary or hex representation I don't know.

Graphics buffers are arranged to match the natural order of rasterization - left to right, top to bottom, and it is the most efficient way to address a bit in a field of arbitrary length.