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The Java language provides two primitive types, {{float}} and {{double}}, which "are conceptually associated with the single-precision 32-bit and double-precision 64-bit format IEEE 754 values and operations as specified in _IEEE Standard for Binary Floating-Point Arithmetic_, ANSI/IEEE Standard 754-1985 (IEEE, New York)" (\[[JLS 2005|AA.Bibliography#JLS 05]\]. [Section 4.2.3|http://java.sun.com/docs/books/jls/third_edition/html/typesValues.html#4.2.3] "Floating-Point Types, Formats, and Values"). Each of the floating point types has a fixed, limited number of mantissa bits. Consequently, it is impossible to precisely represent any irrational number (_e.g._ pi). Further, because these types use a binary mantissa, they cannot precisely represent many finite decimal numbers, such as 1/10, because these numbers have repeating binary representations. |
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