sin_reduce_()

template<typename F>

F fl::detail::sin_reduce_ ( F x )

inline

Definition at line 184 of file math.cpp.hpp.

                                      {
    const F kPi      = F(3.14159265358979323846);
    const F kTwoPi   = F(6.28318530717958647692);
    const F kPiHalf  = F(1.57079632679489661923);
    // Reduce to [-π, π]: subtract floor(x / 2π) * 2π.
    // For the FastLED use cases we expect |x| < ~100, so this loop runs a
    // bounded number of times. For pathological inputs we cap iterations.
    int guard = 32;
    while (x > kPi && guard > 0) { x -= kTwoPi; --guard; }
    while (x < -kPi && guard > 0) { x += kTwoPi; --guard; }
    // Map to [-π/2, π/2] using sin(π - x) = sin(x).
    if (x > kPiHalf)  x = kPi - x;
    if (x < -kPiHalf) x = -kPi - x;
    // [-π/2, π/2] -- the polynomial works fine here (max |x| ≈ 1.57).
    return sin_poly_quarterturn_(x);
}

References FL_NOEXCEPT, sin_poly_quarterturn_(), and fl::x.

Referenced by cos_reduce_(), fl::sin_impl_double(), fl::sin_impl_float(), fl::tan_impl_double(), and fl::tan_impl_float().

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