f64

f64 is a 64-bit floating-point number used in computing to represent real numbers with double precision. It follows the IEEE 754 standard for double-precision binary floating-point arithmetic. In many programming languages, f64 denotes the canonical 64-bit floating type (for example, Rust uses f64; Julia uses Float64); C and C++ typically expose the same representation as double, while Java uses Double as an object wrapper.

Bit layout: f64 uses 1 sign bit, 11 exponent bits, and 52 fraction bits. The exponent uses a bias of 1023. For normal numbers, the significand is 1.F where F is the 52-bit fraction; subnormal numbers have an exponent of zero and no implicit leading 1.

Range and precision: the largest finite value is about 1.7976931348623157e308, and the smallest positive normalized value is about 2.2250738585072014e-308. Subnormal numbers extend the range toward zero down to approximately 4.9406564584124654e-324. The machine epsilon is about 2.220446049250313e-16, reflecting roughly 15 to 17 decimal digits of precision (53 bits of significand).

Special values: exponent all ones with a nonzero significand yields NaN; exponent all ones with zero significand yields +Infinity or -Infinity; exponent all zeros with all-zero significand yields zero; exponent all zeros with a nonzero significand yields subnormal numbers.

Usage and considerations: f64 is widely supported and optimized in hardware, making it the default choice for most numerical tasks that require real numbers, from scientific computing to graphics. Be mindful of rounding errors, cancellation, and decimal-to-binary conversion issues (for example, 0.1 has no exact representation in f64). Some languages offer specialized helpers for numeric stability and precise comparisons.