Pentium FDIV bug

The Pentium FDIV bug is the most famous (or infamous) of the Intel microprocessor bugs. It was caused by an error in a lookup table that was a part of Intel's SRT algorithm that was to be faster and more accurate.

With a goal to boost the execution of floating-point scalar code by 3 times and vector code by 5 times, compared to the 486DX chip, Intel decided to use the SRT algorithm that can generate two quotient bits per clock cycle, while the traditional 486 shift-and-subtract algorithm was generating only one quotient bit per cycle. This SRT algorithm uses a lookup table to calculate the intermidiate quotients necessary for floating-point division. Intel's lookup table consists of 1066 table entries, of which, due to a programming error, five were not downloaded into the programmable logic array (PLA). When any of these five cells is accessed by the floating point unit (FPU), it (the FPU) fetches zero instead of +2, which was supposed to be contained in the "missing" cells. This throws off the calculation and results in a less precise number than the correct answer(Byte Magazine, March 1995).

At its worst, this error can occur as high as the fourth significant digit of a decimal number, but the possibilities of this happening are 1 in 360 billion. It is most common that the error appears in the 9th or 10th decimal digit, which yields a chance of this happening of 1 in 9 billion.

Intel has clasified the bug (or the flaw, as they refer to it) with the following characteristics (Intel):

Furthermore, the bug affects any instruction that references the lookup table or calls FDIV. Related instructions that are affected by the bug are FDIVP, FDIVR, FDIVRP, FIDIV, FIDIVR, FPREM, and FPREM1. The instructions FPTAN and FPATAN are also susceptible. The instructions FYL2X, FYL2XP1, FSIN, FCOS, and FSINCOS, were a suspect but are now considered safe.

A 3-D plot of the ratio 4195835/3145727 calculated on a Pentium with FDIV bug. The depressed triangular areas indicate where incorrect values have been computed. The correct values all would round to 1.3338, but the returned values are 1.3337, an error in the fifth significant digit. Byte Magazine, March 1995.
Intel has adopted a no-questions-asked replacement policy for its customers with the Pentium FDIV bug. It has also done statistical reasearch and provided information on the bug at its site at