Function sseSinCos

src/OpenColorIO/SSE.h:623–643

Sine and Cosine function The function sincos() is evaluated by computing the cosine of the angle, then computing the sine based on the cosine using a simplified formula. The sign of the sine as well as a better approximation for the sine when the input angle is close to zero is done using some of the temporary values determined during the cosine computation. [in] x the input angle [out] sin_x the

// [out] sin_x the sine of the angle
// [out] cos_x the cosine of the angle
inline void sseSinCos(const __m128 x, __m128& sin_x, __m128& cos_x)
{
    // Using a threshold of 2^-7 for the reduced angle seems to provide
    // a fairly decent precision (16 bits) to the final result.
    static const __m128 SINE_THRESHOLD_SQUARED = _mm_set1_ps( (float) 0.00006103515625 );

    __m128 xr, xr2, flip_sign_cos_x;
    __sse_cos__(x, cos_x, xr, xr2, flip_sign_cos_x);

    // When cos(x) becomes too close to 1, the sin(x) evaluation contains too
    // much error. However, in this case, sin(x) ~ x, and we can use xr to 
    // approximate sin(x) instead.
    __m128 sin_x2 = _mm_sub_ps(EONE, _mm_mul_ps(cos_x, cos_x));
    sin_x2 = sseSelect(_mm_cmpgt_ps(xr2, SINE_THRESHOLD_SQUARED), sin_x2, xr2);
    sin_x = _mm_sqrt_ps(sin_x2);

    // Flip the sign of sin(x) if the angle was in quadrants 3 or 4.
    __m128 xr_sign = _mm_and_ps(xr, ESIGN_MASK);
    __m128 flip_sign_sin_x = _mm_xor_ps(flip_sign_cos_x, xr_sign);
    sin_x = _mm_xor_ps(sin_x, flip_sign_sin_x);
}

// Scalar version of sseSinCos
inline void sseSinCos(const float x, float& sin_x, float& cos_x)