singleprecision

Single precision, formally the 32-bit binary32 floating-point format defined by the IEEE 754 standard, uses 32 bits: 1 sign bit, 8 exponent bits, and 23 fraction bits. The exponent is biased by 127. For normal numbers, the significand is 1.f where f is the 23-bit fraction; subnormal numbers use an exponent of zero and a leading zero in the significand. Special values include infinity and NaN.

Value range and precision: The format can represent numbers approximately from 1.4 × 10^-45 up to 3.4 × 10^38. It provides about 7.2 decimal digits of precision. Denormal numbers allow gradual underflow near zero.

Usage and performance: Single precision is widely used where memory or bandwidth is constrained, such as graphics processing, signal processing on embedded systems, and many programming languages when declaring float types. It is typically faster or more cache-friendly than double precision on many architectures; however, it loses precision and can cause rounding errors.

Limitations and care: Operations can accumulate rounding error; comparisons and equality are tricky; conversion between decimal and binary can introduce errors; not suitable for high-precision calculations. All arithmetic follows IEEE 754 rounding modes.

Standards and naming: In software, single precision is often referred to as binary32 or simply float (for languages that implement IEEE 754 by default). The IEEE 754 standard has defined this format since 1985, with revisions in 2008 that clarified behavior and special values. Other precisions exist, such as double precision (binary64) and half-precision (binary16).