binary32

Binary32 is the IEEE 754 standard for 32-bit floating-point numbers, commonly implemented as the single-precision format in many programming languages and hardware. It consists of 32 bits divided into a sign bit, eight exponent bits, and 23 fraction bits. The value of a normal number is (-1)^sign * (1.fraction) * 2^(exponent-127), where the exponent is stored with a bias of 127. When the exponent field is zero, the number is denormalized and has the value (-1)^sign * 0.fraction * 2^(-126). In that case there is no implicit leading 1. If the exponent field is all ones (255), the value represents infinity when the fraction is zero, or NaN (not a number) otherwise. Subnormal representations allow gradual underflow toward zero.

The largest finite value is approximately 3.4028235e38, and the smallest positive normal is about 1.17549435e-38; the smallest positive subnormal is about 1.40129846e-45. The format provides roughly 7 decimal digits of precision and covers a wide dynamic range, making it suitable for graphics, real-time systems, and general numerical tasks. It uses 4 bytes per value and is generally faster and more memory-efficient than double-precision formats.

IEEE 754 rounding modes apply to binary32 operations, and results may suffer from rounding error, cancellation, overflow, or underflow. Special care is needed when comparisons, equality checks, or operations near zero occur. Variants include binary16 and binary64, with binary32 occupying a middle ground for performance and precision.