Примеры Зигфрида Румпа.

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Ошибочные вычисления с плавающей запятой:

• Compute a*a - 2*b*b where a = 665857 and b = 470832 are of type float. Then compute a*a - 2.0*b*b. Repeat with type double. Java answers with float: 0.0 and 11776.0. Java answers with double: 1.0. Exact answer: 1.0.
• Compute 9x4 - y4 + 2y2 where x = 10864 and y = 18817 are of type double. Java answer: 2.0. Exact answer: 1.0.
• Compute p(x) = 8118x4 - 11482x3 + x2 + 5741x - 2030 where x = 0.707107 is of type float and double. Java answer for float: 1.2207031E-4. Java answer for double: -1.9554136088117957E-11. Exact answer: -1.91527325270... * 10^-7.

Отсюда.