{"channel":"misc","content":"a link too good to pass up: https://www.righto.com/2024/12/this-die-photo-of-pentium-shows.html\r\n\r\n<< In 1993, Intel released the high-performance Pentium processor, the start of the long-running Pentium line. The Pentium had many improvements over the previous processor, the Intel 486, including a faster floating-point division algorithm. A year later, Professor Nicely, a number theory professor, was researching reciprocals of twin prime numbers when he noticed a problem: his Pentium sometimes generated the wrong result when performing floating-point division. Intel considered this \"an extremely minor technical problem\", but much to Intel's surprise, the bug became a large media story. After weeks of criticism, mockery, and bad publicity, Intel agreed to replace everyone's faulty Pentium chips, costing the company $475 million. ... In this article, I discuss the Pentium's division algorithm, show exactly where the bug is on the Pentium chip, take a close look at the circuitry, and explain what went wrong. In brief, the division algorithm uses a lookup table. In 1994, Intel stated that the cause of the bug was that five entries were omitted from the table due to an error in a script. However, my analysis shows that 16 entries were omitted due to a mathematical mistake in the definition of the lookup table. Five of the missing entries trigger the bug\u2014 also called the FDIV bug after the floating-point division instruction \"FDIV\"\u2014while 11 of the missing entries have no effect. >>","created_at":"2025-01-04T23:38:40.448265","id":66,"llm_annotations":{},"parent_id":null,"processed_content":"

a link too good to pass up: https://www.righto.com/2024/12/this-die-photo-of-pentium-shows.html\r

\n

In 1993, Intel released the high-performance Pentium processor, the start of the long-running Pentium line. The Pentium had many improvements over the previous processor, the Intel 486, including a faster floating-point division algorithm. A year later, Professor Nicely, a number theory professor, was researching reciprocals of twin prime numbers when he noticed a problem: his Pentium sometimes generated the wrong result when performing floating-point division. Intel considered this \"an extremely minor technical problem\", but much to Intel's surprise, the bug became a large media story. After weeks of criticism, mockery, and bad publicity, Intel agreed to replace everyone's faulty Pentium chips, costing the company $475 million. ... In this article, I discuss the Pentium's division algorithm, show exactly where the bug is on the Pentium chip, take a close look at the circuitry, and explain what went wrong. In brief, the division algorithm uses a lookup table. In 1994, Intel stated that the cause of the bug was that five entries were omitted from the table due to an error in a script. However, my analysis shows that 16 entries were omitted due to a mathematical mistake in the definition of the lookup table. Five of the missing entries trigger the bug\u2014 also called the FDIV bug after the floating-point division instruction \"FDIV\"\u2014while 11 of the missing entries have no effect.

","quotes":[],"subject":"strange arithmetic"}