strange arithmetic

Hide hard words

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

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