slerp: investigate accuracy of slerp

[myfreeer]

The current used impl of slerp uses sinTheta = sqrtf(1.0f - cosTheta * cosTheta); to approximate sine from cosine, accuracy is fine for runtime interpolation, but futher investigation is needed that would the accuracy match the needed of resampling?
Also, how much would this impact the performance?
Code here: https://github.com/recp/cglm/blob/44268d24f93f65d280a20ead64d96035cf91f765/include/cglm/quat.h#L727
Discussion about this on stackoverflow: https://stackoverflow.com/a/2683608

Some third-patry math libs that uses acos + sin:

• https://github.com/g-truc/glm/blob/b3f87720261d623986f164b2a7f6a0a938430271/glm/ext/quaternion_common.inl#L70-L71
• https://github.com/redorav/hlslpp/blob/3305152eda7f70a03e88e5899f399ff188bd1a78/include/hlsl%2B%2B_quaternion.h#L156-L159
• https://github.com/boostorg/qvm/blob/e659dc47a6369504b7d607f3749de1e808887e61/include/boost/qvm/quat_operations.hpp#L727-L728
• https://github.com/godotengine/godot/blob/9f12e7b52d944281a39b7d3a33de6700c76cc23a/core/math/quaternion.cpp#L135-L136
• https://github.com/felselva/mathc/blob/d672725203fc80f6f79fba64533b87d51c32d714/mathc.c#L2062

Some third-party math libs that uses this algorithm:

• https://github.com/MartinWeigel/Quaternion/blob/73fd3ee23a54abae387c6c0da21886ca755be606/Quaternion.c#L254-L255
• https://github.com/JuliaGeometry/Quaternions.jl/blob/b482c33ffc8789eff949bfdb10479aaae703b825/src/Quaternion.jl#L382
• https://github.com/microsoft/DirectXMath/blob/332fb99d07d64f3b4fa89fafb4f303b758420749/Inc/DirectXMathMisc.inl#L323-L328

Some uses other algorithm:

• https://github.com/Kazade/kazmath/blob/48dbc191da47880ea6708b0a7b3c7b69b6352cad/kazmath/quaternion.c#L373

Extra:
Vectorized sin might be used to accelerate the sinf, maybe something like:

• https://github.com/shibatch/sleef/blob/85440a5e87dae36ca1b891de14bc83b441ae7c43/src/libm/sleefsimdsp.c#L912
• https://web.archive.org/web/20130927121234/http://devmaster.net/posts/9648/fast-and-accurate-sine-cosine
• https://github.com/RJVB/sse_mathfun/blob/0f462645698320643decdb5f79d211733b2a97d6/sse_mathfun.h#L525
• https://github.com/brendanashworth/approxmath/blob/e082b246d801447295c862c7351b9a5dc45e779d/src/approxmath/np/simd_math_prims.h#L201
• https://github.com/parallella/pal/blob/bd9389f14fe16db4d963088a530a4f4908f42b01/src/math/p_sin.c#L20
• https://github.com/JishinMaster/simd_utils/blob/9f8bc0f1749bcf7b7a7a67830b3d082ea225fc56/sse_mathfun.h#L193
• https://github.com/nfrechette/rtm/blob/5cba8603d2efb32895e2961e91f56999f04ed79b/tools/bench/sources/bench_vector_sin.cpp#L31
• https://github.com/niello/deusexmachina/blob/a0a78df3181cab1b27c55f51e379a52f80796099/DEM/Low/src/Animation/Inertialization.cpp#L64
• https://github.com/vectorclass/version2/blob/9d324e13457cf67b44be04f49a4a0036bb188a89/vectormath_trig.h#L230
• https://github.com/NVIDIAGameWorks/MathLib/blob/e2d9d65bfb8448ca9059dd4b69eea3811edcac6d/IntrinEmu.h#L2108
• https://bitbucket.org/eschnett/vecmathlib/src/master/mathfuncs_sin.h

[myfreeer]

It shows ~11% slower on wasm, ~10% slower on simd, ~3% less frames.

before:

after:

[kzhsw]

https://github.com/amd/aocl-libm-ose/blob/master/src/optmized/vec/vrs4_sinf.c