doubleprecision

Double precision is a common format for representing real numbers in computing. In IEEE 754, a double-precision floating-point number uses 64 bits and provides about 15 to 17 decimal digits of precision with a wide dynamic range. It is widely supported by hardware and programming languages, and is often the default floating-point type for 64-bit arithmetic, typically referred to as double.

The 64 bits are laid out as 1 sign bit, 11 exponent bits, and 52 fraction bits. The significand is interpreted with an implicit leading 1 for normal numbers, yielding 53 bits of precision. The exponent uses a bias of 1023, so the actual exponent equals the stored value minus 1023. Exponent values all zero or all ones are reserved for special numbers: zero and subnormals, infinities, and NaNs.

Finite double values range approximately from -1.7976931348623157e308 to +1.7976931348623157e308, with the smallest positive normal value around 2.2250738585072014e-308 and subnormals extending down to about 4.9406564584124654e-324.

In practice, double precision offers a balance between accuracy and resource use. It is eight bytes per value, enabling efficient computation and storage on most modern CPUs. However, it is subject to rounding errors and representation limits for many decimal fractions; arithmetic can yield rounding, cancellation, or propagation of error, and special values such as NaN and infinities can arise from exceptional conditions or invalid operations.

Standardization under IEEE 754 also defines behavior for arithmetic, rounding modes, and exceptional conditions, ensuring portability across platforms. Many languages expose this format as the double type, while others use language-specific aliases or rely on underlying hardware support.