Sincosdouble

Sincosdouble is a term used in numerical computing to denote a function that computes both sine and cosine of a double-precision angle in a single call. The primary goal is to improve performance and numerical consistency by sharing the same input reduction and internal representation for both trigonometric values, instead of evaluating sin and cos separately.

Typical interfaces: in C-like languages it can be declared as void sincosdouble(double x, double* s, double* c); or as a function returning a pair of doubles in modern C++ style. The function writes into the provided output variables or returns a pair containing sin(x) and cos(x). The exact naming and signature vary by library, but the concept remains the same: one call yields both results.

Algorithmic approach: most implementations perform a single argument reduction of x modulo 2π to a small, well-conditioned range, then evaluate sin and cos using a pair of closely linked polynomial or rational approximations, or a small table with polynomial corrections. By computing sin and cos from the same reduced value, the results share rounding decisions, reducing the risk that one value is significantly less accurate than the other.

Handling special inputs: inputs that are NaN or infinite generally yield NaN for both sine and cosine, following IEEE 754 rules; some implementations may propagate domain or range errors for extreme arguments. Thread safety and portability depend on the library and compiler.

Applications: widely used in graphics, physics engines, simulations, and other performance-sensitive code that requires both sine and cosine of the same angle without redundant computation.

See also: sincos, sin, cos, double-precision trigonometric routines.