log1pf

log1pf is a function in the C standard math library that computes the natural logarithm of 1 plus a floating-point input, specifically for float precision. It is declared in <math.h> with the prototype float log1pf(float x). The function is designed to provide higher accuracy than a straightforward call to logf(1+x) when x is small, by reducing cancellation errors that can occur near x = 0.

Domain and behavior: The mathematical domain is -1 < x. When x equals -1, the result is -infinity, since log(0) is undefined but approaches negative infinity. For x < -1 the result is NaN, indicating a domain error. If x is NaN, +Inf, or -Inf, the function propagates NaN or yields the appropriate IEEE 754 result (for example, log1pf(+Inf) is +Inf). For large positive x, the result approximates log(1+x) as expected. Floating-point exceptions and errno behavior follow the host system’s C library conventions.

Implementation notes: Implementations typically use a range reduction combined with carefully chosen polynomial or rational approximations to compute log(1+x) accurately for small x while maintaining performance. log1pf is part of a family that includes log1p for double precision and log1pl for long double, each providing similar accuracy benefits for their respective types.

See also: log1p, logf, log, and the broader set of special mathematical functions in the C standard library.