fp32

FP32, or 32-bit floating-point, is the binary32 format defined by the IEEE 754 standard. It encodes numbers with 1 sign bit, 8 exponent bits, and 23 fraction bits, totaling 32 bits. The value for normal numbers is (-1)^sign × (1 + mantissa/2^23) × 2^(exponent - 127), where the exponent bias is 127. When the exponent field is zero, the number is subnormal or zero; when the exponent is all ones (255), the number represents infinity or NaN.

Normal values span roughly -3.4028235 × 10^38 to +3.4028235 × 10^38. Subnormal numbers fill the tiny subnormal range down to about 1.4 × 10^−45. FP32 provides about 24 bits of precision (including the implicit leading 1), equivalent to roughly 7 decimal digits. The default rounding mode is round to nearest, ties to even, and NaN/Inf are defined for exceptional cases.

In computing, FP32 is widely supported by CPUs and GPUs, with a 4-byte memory footprint per value. It offers faster arithmetic and lower memory use than FP64, at the cost of reduced precision. FP32 is commonly used in graphics pipelines, simulations, and especially in many machine learning workloads, where its balance of range and precision is adequate. Programming languages expose it as float or float32 (e.g., numpy.float32).

Compared with FP64 (double precision), FP32 has a smaller mantissa and exponent range, trading accuracy for speed and memory. Compared with FP16 (half precision), FP32 provides higher precision and dynamic range. Developers must beware rounding errors, cancellation, underflow/overflow, and special values such as NaN and Inf when performing calculations.