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Add fastMix() and fastSlerp() implementations.
These have stricter pre-conditions than standard mix() and slerp() - 1) Input quaternions must be unit length. - 2) The interpolation factor (a) must be in the range [0, 1] None of these restrictions should be too bad. The reason for these is that it uses fastAcos() and fastSin(), both of which have a limited allowable range. In my contrived tests, I observed about a 10x improvement over the standard versions. This is mostly because of the faster acos/sin operations. The fastSin(__m128) implementation also helps here because it can do four fastSin() operations simultaneously using SSE (mix() and slerp() each need three).
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@ -41,6 +41,7 @@
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// Dependency:
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#include "../glm.hpp"
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#include "../gtc/quaternion.hpp"
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#include "../gtx/fast_trigonometry.hpp"
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#if(GLM_ARCH != GLM_ARCH_PURE)
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@ -223,7 +224,7 @@ namespace detail
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/// @param a Interpolation factor. The interpolation is defined beyond the range [0, 1].
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/// @tparam T Value type used to build the quaternion. Supported: half, float or double.
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/// @see gtc_quaternion
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/// @see - slerp(detail::tquat<T> const & x, detail::tquat<T> const & y, T const & a)
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/// @see - slerp(detail::fquatSIMD const & x, detail::fquatSIMD const & y, T const & a)
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detail::fquatSIMD mix(
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detail::fquatSIMD const & x,
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detail::fquatSIMD const & y,
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@ -255,6 +256,35 @@ namespace detail
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detail::fquatSIMD const & y,
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float const & a);
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/// Faster spherical linear interpolation of two unit length quaternions.
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///
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/// This is the same as mix(), except for two rules:
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/// 1) The two quaternions must be unit length.
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/// 2) The interpolation factor (a) must be in the range [0, 1].
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///
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/// This will use the equivalent to fastAcos() and fastSin().
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///
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/// @see gtc_quaternion
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/// @see - mix(detail::fquatSIMD const & x, detail::fquatSIMD const & y, T const & a)
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detail::fquatSIMD fastMix(
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detail::fquatSIMD const & x,
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detail::fquatSIMD const & y,
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float const & a);
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/// Identical to fastMix() except takes the shortest path.
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///
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/// The same rules apply here as those in fastMix(). Both quaternions must be unit length and 'a' must be
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/// in the range [0, 1].
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///
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/// @see - fastMix(detail::fquatSIMD const & x, detail::fquatSIMD const & y, T const & a)
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/// @see - slerp(detail::fquatSIMD const & x, detail::fquatSIMD const & y, T const & a)
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detail::fquatSIMD fastSlerp(
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detail::fquatSIMD const & x,
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detail::fquatSIMD const & y,
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float const & a);
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/// Returns the q conjugate.
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///
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/// @see gtc_quaternion
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@ -292,6 +322,11 @@ namespace detail
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float const & z);
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// TODO: Move this to somewhere more appropriate. Used with fastMix() and fastSlerp().
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/// Performs the equivalent of glm::fastSin() on each component of the given __m128.
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__m128 fastSin(__m128 x);
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/// @}
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}//namespace glm
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@ -423,9 +423,6 @@ GLM_FUNC_QUALIFIER detail::fquatSIMD mix
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// Compared to the naive SIMD implementation below, this scalar version is consistently faster. A non-naive SSE-optimized implementation
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// will most likely be faster, but that'll need to be left to people much smarter than I.
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//
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// The issue, I think, is loading the __m128 variables with initial data. Can probably be replaced with an SSE-optimized approximation of
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// glm::sin(). Maybe a fastMix() function would be better for that?
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float s0 = glm::sin((1.0f - a) * angle);
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float s1 = glm::sin(a * angle);
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@ -495,6 +492,73 @@ GLM_FUNC_QUALIFIER detail::fquatSIMD slerp
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}
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}
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GLM_FUNC_QUALIFIER detail::fquatSIMD fastMix
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(
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detail::fquatSIMD const & x,
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detail::fquatSIMD const & y,
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float const & a
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)
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{
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float cosTheta = dot(x, y);
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if (cosTheta > 1.0f - glm::epsilon<float>())
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{
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return _mm_add_ps(x.Data, _mm_mul_ps(_mm_set1_ps(a), _mm_sub_ps(y.Data, x.Data)));
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}
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else
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{
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float angle = glm::fastAcos(cosTheta);
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__m128 s = glm::fastSin(_mm_set_ps((1.0f - a) * angle, a * angle, angle, 0.0f));
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__m128 s0 = _mm_shuffle_ps(s, s, _MM_SHUFFLE(3, 3, 3, 3));
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__m128 s1 = _mm_shuffle_ps(s, s, _MM_SHUFFLE(2, 2, 2, 2));
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__m128 d = _mm_div_ps(_mm_set1_ps(1.0f), _mm_shuffle_ps(s, s, _MM_SHUFFLE(1, 1, 1, 1)));
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return _mm_mul_ps(_mm_add_ps(_mm_mul_ps(s0, x.Data), _mm_mul_ps(s1, y.Data)), d);
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}
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}
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GLM_FUNC_QUALIFIER detail::fquatSIMD fastSlerp
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(
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detail::fquatSIMD const & x,
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detail::fquatSIMD const & y,
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float const & a
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)
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{
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detail::fquatSIMD z = y;
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float cosTheta = dot(x, y);
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if (cosTheta < 0.0f)
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{
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z = -y;
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cosTheta = -cosTheta;
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}
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if(cosTheta > 1.0f - epsilon<float>())
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{
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return _mm_add_ps(x.Data, _mm_mul_ps(_mm_set1_ps(a), _mm_sub_ps(y.Data, x.Data)));
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}
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else
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{
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float angle = glm::fastAcos(cosTheta);
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__m128 s = glm::fastSin(_mm_set_ps((1.0f - a) * angle, a * angle, angle, 0.0f));
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__m128 s0 = _mm_shuffle_ps(s, s, _MM_SHUFFLE(3, 3, 3, 3));
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__m128 s1 = _mm_shuffle_ps(s, s, _MM_SHUFFLE(2, 2, 2, 2));
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__m128 d = _mm_div_ps(_mm_set1_ps(1.0f), _mm_shuffle_ps(s, s, _MM_SHUFFLE(1, 1, 1, 1)));
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return _mm_mul_ps(_mm_add_ps(_mm_mul_ps(s0, x.Data), _mm_mul_ps(s1, y.Data)), d);
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}
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}
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GLM_FUNC_QUALIFIER detail::fquatSIMD conjugate
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(
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detail::fquatSIMD const & q
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@ -544,4 +608,22 @@ GLM_FUNC_QUALIFIER detail::fquatSIMD angleAxisSIMD
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}
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GLM_FUNC_QUALIFIER __m128 fastSin(__m128 x)
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{
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static const __m128 c0 = _mm_set1_ps(0.16666666666666666666666666666667f);
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static const __m128 c1 = _mm_set1_ps(0.00833333333333333333333333333333f);
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static const __m128 c2 = _mm_set1_ps(0.00019841269841269841269841269841f);
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__m128 x3 = _mm_mul_ps(x, _mm_mul_ps(x, x));
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__m128 x5 = _mm_mul_ps(x3, _mm_mul_ps(x, x));
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__m128 x7 = _mm_mul_ps(x5, _mm_mul_ps(x, x));
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__m128 y0 = _mm_mul_ps(x3, c0);
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__m128 y1 = _mm_mul_ps(x5, c1);
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__m128 y2 = _mm_mul_ps(x7, c2);
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return _mm_sub_ps(_mm_add_ps(_mm_sub_ps(x, y0), y1), y2);
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}
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}//namespace glm
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