Pentium Micro Flaw
Jamai Wilson
The Pentium microprocessor flaw was discovered in June, 1994. The Pentium microprocessor is the CPU for what was once possibly the widest-selling personal computer. Unlike previous CPUs that Intel put on the market, the 486DX and Pentium chips included a floating-point unit (FPU), which is also known as a math coprocessor. Previous Intel CPUs performed arithmetic using integers; programs that used floating-point numbers (non-integers like 2.5 or 3.14) needed to tell the chip how to divide them using integer arithmetic. The 486DX and Pentium chips have these instructions built into the chip, in their FPUs, which allowed them to be much faster for intense numerical calculations, more complex, and more expensive. All Pentiums manufactured that fall had errors in the on-chip FPU instructions for division. This caused the Pentium’s FPU to incorrectly divide certain floating-point numbers.
Several software packages, including many that do use floating-point numbers, do not actually use a computer’s FPU. These packages fail to show the error. Certain numbers, whose binary representation shows specific bit patterns, divide incorrectly. This is the reason why many users never encountered the division error.
Problem: 4,195,835 – [(4,195,835 / 3,145,727) x 3,145,727]
Correct Calculation: 4,195,835 – [(1.3338204) x 3,145,727] = 0
Pentium’s Calculation: 4,195,835 – [(1.3337391) x 3,145,727] = 256
Deviation: 256 / 4,195,835 = 6.1 x 10^-5, or 61 / 100,000
One can easily test a Pentium using Microsoft’s Windows by using the Windows calculator in scientific mode to compare the numbers above.
The problem was apparent when the chip rounds a number from a previous calculation to get the final result of the impending calculation. For most chips that are in other PCs this task was not uncommon as they could handle numbers up to 16 digits. The Pentium chips, however, were only exact up to 5 digits.
Intel first publicly announced that “an error is
The Pentium microprocessor flaw was discovered in June, 1994. The Pentium microprocessor is the CPU for what was once possibly the widest-selling personal computer. Unlike previous CPUs that Intel put on the market, the 486DX and Pentium chips included a floating-point unit (FPU), which is also known as a math coprocessor. Previous Intel CPUs performed arithmetic using integers; programs that used floating-point numbers (non-integers like 2.5 or 3.14) needed to tell the chip how to divide them using integer arithmetic. The 486DX and Pentium chips have these instructions built into the chip, in their FPUs, which allowed them to be much faster for intense numerical calculations, more complex, and more expensive. All Pentiums manufactured that fall had errors in the on-chip FPU instructions for division. This caused the Pentium’s FPU to incorrectly divide certain floating-point numbers.
Several software packages, including many that do use floating-point numbers, do not actually use a computer’s FPU. These packages fail to show the error. Certain numbers, whose binary representation shows specific bit patterns, divide incorrectly. This is the reason why many users never encountered the division error.
Problem: 4,195,835 – [(4,195,835 / 3,145,727) x 3,145,727]
Correct Calculation: 4,195,835 – [(1.3338204) x 3,145,727] = 0
Pentium’s Calculation: 4,195,835 – [(1.3337391) x 3,145,727] = 256
Deviation: 256 / 4,195,835 = 6.1 x 10^-5, or 61 / 100,000
One can easily test a Pentium using Microsoft’s Windows by using the Windows calculator in scientific mode to compare the numbers above.
The problem was apparent when the chip rounds a number from a previous calculation to get the final result of the impending calculation. For most chips that are in other PCs this task was not uncommon as they could handle numbers up to 16 digits. The Pentium chips, however, were only exact up to 5 digits.
Intel first publicly announced that “an error is