/floʊt ˈsɪksˌtiːfɔːr/
noun … “a 64-bit double-precision floating-point number.”
Float64 is a numeric data type that represents real numbers using 64 bits according to the IEEE 754 standard. It allocates 1 bit for the sign, 11 bits for the exponent, and 52 bits for the fraction (mantissa), providing approximately 15–17 decimal digits of precision. This expanded precision compared to Float32 allows for highly accurate computations in scientific simulations, financial calculations, and any context where rounding errors must be minimized.
Arithmetic on Float64 follows IEEE 754 rules, handling rounding, overflow, underflow, and special values such as Infinity and NaN. The large exponent range enables representation of extremely large or extremely small numbers, making Float64 suitable for applications like physics simulations, statistical analysis, numerical linear algebra, and engineering calculations.
Float64 is often used alongside other numeric types such as Float32, INT32, UINT32, INT64, and UINT64. While Float64 consumes more memory than Float32 (8 Bytes per value versus 4), it reduces the accumulation of rounding errors in iterative computations, providing stable results over long sequences of calculations.
In programming and scientific computing, Float64 is standard for high-precision tasks. Libraries for numerical analysis, such as Julia, Python’s NumPy, or MATLAB, default to Float64 arrays for calculations that require accuracy. GPU programming may still prefer Float32 for speed, but Float64 is critical when precision outweighs performance.
Memory layout is predictable: each Float64 occupies exactly 8 Bytes, and contiguous arrays enable optimized vectorized operations using SIMD (Single Instruction, Multiple Data). This allows CPUs and GPUs to perform high-performance batch computations while maintaining numerical stability.
Programmatically, Float64 supports arithmetic, comparison, and mathematical functions including trigonometry, exponentials, logarithms, and linear algebra routines. Its wide dynamic range allows accurate modeling of physical phenomena, large datasets, and complex simulations that would quickly lose fidelity with Float32.
An example of Float64 in practice:
using Julia
x = Float64[1.0, 2.5, 3.14159265358979]
y = x .* 2.0
println(y) # outputs [2.0, 5.0, 6.28318530717958]The intuition anchor is that Float64 is a precise numeric container: large, accurate, and robust, capable of representing extremely small or large real numbers without significant loss of precision, making it essential for scientific and financial computing.