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Unit 5 Analysis 1 : Pentium Flaw
The Pentium microprocessor is the CPU (central processing unit) for the widest selling personal computers. Unlike previous CPUs made by Intel, the 486DX and Pentium chips came along with a floating-point unit (FPU) also known as the math co-processor. Previous Intel CPUs did all their arithmetic using integers; programs that used floating-point numbers (non-integers like 2.5 or 3.14) needed to tell the chip how (for example) to divide them using integer arithmetic. The 486DX and Pentium chips have these instructions built into the chip, in their FPUs. This makes them much faster for intense numerical calculations, more complex, and more expensive. The problem for Intel is that all Pentiums manufactured until sometime this fall had errors in the on-chip FPU instructions for division. This caused the Pentium's FPU to incorrectly divide certain floating-point numbers.
Many software packages, including many that do use floating-point numbers, don't actually use a computer's FPU. These packages don't show the error. Also, only certain numbers (whose binary representation show specific bit patterns) divide incorrectly. Consequently many users may never encounter the division error. The most famous example and the worst well-known case is 4195835/3145727, discovered by Tim Coe of Vitesse Semiconductors. The correct value is 1.33382 to 6 sig. figs, while the flawed Pentium's floating-point unit computed 1.33374 to 6 sig figs, a relative error of 0.006%. One can easily test a Pentium using Microsoft's Windows and this example: Use the Windows calculator in scientific mode to divide Coe's numbers and compare to the numbers above.
In summer/fall of 1994, Dr. Thomas Nicely, a math professor at Lynchburg College in Virginia discovered some errors in his calculations. He cross-checked the same calculation on a 486 CPU and the results turned out

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