Pentium FDIV bug

The Pentium FDIV bug is a hardware bug affecting the floating-point unit (FPU) of the early Intel Pentium processors. Because of the bug, the processor would return incorrect binary floating point results when dividing certain pairs of high-precision numbers. The bug was discovered in 1994 by Thomas R. Nicely, a professor of mathematics at Lynchburg College. Missing values in a lookup table used by the FPU's floating-point division algorithm led to calculations acquiring small errors. While these errors would in most use-cases only occur rarely and result in small deviations from the correct output values, in certain circumstances the errors can occur frequently and lead to more significant deviations. The severity of the FDIV bug is debated. Though rarely encountered by most users (Byte magazine estimated that 1 in 9 billion floating point divides with random parameters would produce inaccurate results), both the flaw and Intel's initial handling of the matter were heavily criticized by the tech community. In December 1994, Intel recalled the defective processors in what was the first full recall of a computer chip. In its 1994 annual report, Intel said it incurred "a $475 million pre-tax charge ... to recover replacement and write-off of these microprocessors." In order to improve the speed of floating-point division calculations on the Pentium chip over the 486DX, Intel opted to replace the shift-and-subtract division algorithm with the Sweeney, Robertson, and Tocher (SRT) algorithm. The SRT algorithm can generate two bits of the division result per clock cycle, whereas the 486's algorithm could only generate one. It is implemented using a programmable logic array with 2,048 cells, of which 1,066 cells should have been populated with one of five values: −2, −1, 0, +1, +2. When the original array for the Pentium was compiled, five values were not correctly downloaded into the equipment that etches the arrays into the chips – thus five of the array cells contained zero when they should have contained +2.

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Pentium FDIV bug

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