| Pré. | Proc. |
cos
Circular cosine.SYNOPSIS:
double x, y, cos();
y = cos(x);
DESCRIPTION:
Range reduction is into intervals of pi/4. The reduction error is nearly eliminated by contriving an extended precision modular arithmetic.
Two polynomial approximating functions are employed.
Between 0 and pi/4 the cosine is approximated by:
1 - x**2 Q(x**2).
Between pi/4 and pi/2 the sine is represented as:
x + x**3 P(x**2).
ACCURACY:
Relative error:
arithmetic domain # trials peak rms
IEEE -1.07e9,+1.07e9 130000 2.1e-16 5.4e-17
DEC 0,+1.07e9 17000 3.0e-17 7.2e-18