fixed32

Fixed32 refers to a family of 32-bit fixed-point numerical formats used to represent real numbers with a fixed binary point. In fixed32, a fixed number of lower bits are allocated to the fractional part while the remaining bits store the integer part. The arrangement is commonly described as a Qm.n format, where m is the number of integer bits and n is the number of fractional bits, with m+n+1 = 32 including the sign bit. Common variants include Q16.16 and Q1.31.

In Q16.16, values range roughly from -32768 to 32767.999... with a resolution of 1/65536; in Q1.31, the range is -1 to just under 1 with a resolution of 1/2^31.

Arithmetic in fixed32 uses scaled integers. Fixed32 numbers are stored as 32-bit integers scaled by 2^n. Addition and subtraction follow standard integer rules. Multiplication requires a 64-bit intermediate value and then a shift right by n bits to restore the fixed-point scale. Division similarly uses a 64-bit intermediate. Overflow is a concern, and some implementations apply saturation or wrap-around. Rounding during conversions helps maintain accuracy.

Conversions between representations are straightforward: from integer, multiply by 2^n; to integer, round or truncate. From floating-point, multiply by 2^n and round to the nearest fixed32 value; to floating-point, divide by 2^n.

Applications of fixed32 include embedded systems, digital signal processing, graphics, and performance-critical code where floating-point hardware is unavailable or undesirable. It offers deterministic arithmetic and predictable performance at the cost of limited range and precision. Variants beyond Q16.16 and Q1.31 exist and are chosen to balance memory usage against required precision.