987 lines
31 KiB
C++
987 lines
31 KiB
C++
// Jolt Physics Library (https://github.com/jrouwe/JoltPhysics)
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// SPDX-FileCopyrightText: 2021 Jorrit Rouwe
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// SPDX-License-Identifier: MIT
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#include <Jolt/Math/Trigonometry.h>
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#include <Jolt/Math/Vec3.h>
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#include <Jolt/Math/UVec4.h>
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JPH_NAMESPACE_BEGIN
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// Constructor
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Vec4::Vec4(Vec3Arg inRHS) :
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mValue(inRHS.mValue)
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{
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}
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Vec4::Vec4(Vec3Arg inRHS, float inW)
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{
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#if defined(JPH_USE_SSE4_1)
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mValue = _mm_blend_ps(inRHS.mValue, _mm_set1_ps(inW), 8);
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#elif defined(JPH_USE_NEON)
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mValue = vsetq_lane_f32(inW, inRHS.mValue, 3);
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#else
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for (int i = 0; i < 3; i++)
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mF32[i] = inRHS.mF32[i];
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mF32[3] = inW;
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#endif
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}
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Vec4::Vec4(float inX, float inY, float inZ, float inW)
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{
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#if defined(JPH_USE_SSE)
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mValue = _mm_set_ps(inW, inZ, inY, inX);
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#elif defined(JPH_USE_NEON)
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uint32x2_t xy = vcreate_u32(static_cast<uint64>(BitCast<uint32>(inX)) | (static_cast<uint64>(BitCast<uint32>(inY)) << 32));
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uint32x2_t zw = vcreate_u32(static_cast<uint64>(BitCast<uint32>(inZ)) | (static_cast<uint64>(BitCast<uint32>(inW)) << 32));
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mValue = vreinterpretq_f32_u32(vcombine_u32(xy, zw));
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#else
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mF32[0] = inX;
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mF32[1] = inY;
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mF32[2] = inZ;
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mF32[3] = inW;
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#endif
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}
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template<uint32 SwizzleX, uint32 SwizzleY, uint32 SwizzleZ, uint32 SwizzleW>
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Vec4 Vec4::Swizzle() const
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{
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static_assert(SwizzleX <= 3, "SwizzleX template parameter out of range");
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static_assert(SwizzleY <= 3, "SwizzleY template parameter out of range");
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static_assert(SwizzleZ <= 3, "SwizzleZ template parameter out of range");
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static_assert(SwizzleW <= 3, "SwizzleW template parameter out of range");
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#if defined(JPH_USE_SSE)
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return _mm_shuffle_ps(mValue, mValue, _MM_SHUFFLE(SwizzleW, SwizzleZ, SwizzleY, SwizzleX));
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#elif defined(JPH_USE_NEON)
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return JPH_NEON_SHUFFLE_F32x4(mValue, mValue, SwizzleX, SwizzleY, SwizzleZ, SwizzleW);
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#else
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return Vec4(mF32[SwizzleX], mF32[SwizzleY], mF32[SwizzleZ], mF32[SwizzleW]);
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#endif
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}
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Vec4 Vec4::sZero()
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{
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#if defined(JPH_USE_SSE)
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return _mm_setzero_ps();
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#elif defined(JPH_USE_NEON)
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return vdupq_n_f32(0);
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#else
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return Vec4(0, 0, 0, 0);
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#endif
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}
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Vec4 Vec4::sReplicate(float inV)
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{
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#if defined(JPH_USE_SSE)
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return _mm_set1_ps(inV);
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#elif defined(JPH_USE_NEON)
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return vdupq_n_f32(inV);
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#else
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return Vec4(inV, inV, inV, inV);
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#endif
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}
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Vec4 Vec4::sOne()
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{
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return sReplicate(1.0f);
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}
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Vec4 Vec4::sNaN()
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{
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return sReplicate(numeric_limits<float>::quiet_NaN());
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}
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Vec4 Vec4::sLoadFloat4(const Float4 *inV)
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{
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#if defined(JPH_USE_SSE)
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return _mm_loadu_ps(&inV->x);
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#elif defined(JPH_USE_NEON)
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return vld1q_f32(&inV->x);
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#else
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return Vec4(inV->x, inV->y, inV->z, inV->w);
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#endif
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}
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Vec4 Vec4::sLoadFloat4Aligned(const Float4 *inV)
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{
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#if defined(JPH_USE_SSE)
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return _mm_load_ps(&inV->x);
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#elif defined(JPH_USE_NEON)
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return vld1q_f32(&inV->x);
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#else
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return Vec4(inV->x, inV->y, inV->z, inV->w);
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#endif
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}
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template <const int Scale>
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Vec4 Vec4::sGatherFloat4(const float *inBase, UVec4Arg inOffsets)
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{
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#if defined(JPH_USE_SSE)
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#ifdef JPH_USE_AVX2
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return _mm_i32gather_ps(inBase, inOffsets.mValue, Scale);
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#else
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const uint8 *base = reinterpret_cast<const uint8 *>(inBase);
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Type x = _mm_load_ss(reinterpret_cast<const float *>(base + inOffsets.GetX() * Scale));
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Type y = _mm_load_ss(reinterpret_cast<const float *>(base + inOffsets.GetY() * Scale));
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Type xy = _mm_unpacklo_ps(x, y);
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Type z = _mm_load_ss(reinterpret_cast<const float *>(base + inOffsets.GetZ() * Scale));
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Type w = _mm_load_ss(reinterpret_cast<const float *>(base + inOffsets.GetW() * Scale));
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Type zw = _mm_unpacklo_ps(z, w);
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return _mm_movelh_ps(xy, zw);
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#endif
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#else
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const uint8 *base = reinterpret_cast<const uint8 *>(inBase);
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float x = *reinterpret_cast<const float *>(base + inOffsets.GetX() * Scale);
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float y = *reinterpret_cast<const float *>(base + inOffsets.GetY() * Scale);
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float z = *reinterpret_cast<const float *>(base + inOffsets.GetZ() * Scale);
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float w = *reinterpret_cast<const float *>(base + inOffsets.GetW() * Scale);
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return Vec4(x, y, z, w);
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#endif
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}
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Vec4 Vec4::sMin(Vec4Arg inV1, Vec4Arg inV2)
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{
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#if defined(JPH_USE_SSE)
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return _mm_min_ps(inV1.mValue, inV2.mValue);
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#elif defined(JPH_USE_NEON)
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return vminq_f32(inV1.mValue, inV2.mValue);
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#else
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return Vec4(min(inV1.mF32[0], inV2.mF32[0]),
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min(inV1.mF32[1], inV2.mF32[1]),
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min(inV1.mF32[2], inV2.mF32[2]),
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min(inV1.mF32[3], inV2.mF32[3]));
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#endif
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}
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Vec4 Vec4::sMax(Vec4Arg inV1, Vec4Arg inV2)
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{
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#if defined(JPH_USE_SSE)
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return _mm_max_ps(inV1.mValue, inV2.mValue);
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#elif defined(JPH_USE_NEON)
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return vmaxq_f32(inV1.mValue, inV2.mValue);
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#else
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return Vec4(max(inV1.mF32[0], inV2.mF32[0]),
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max(inV1.mF32[1], inV2.mF32[1]),
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max(inV1.mF32[2], inV2.mF32[2]),
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max(inV1.mF32[3], inV2.mF32[3]));
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#endif
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}
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UVec4 Vec4::sEquals(Vec4Arg inV1, Vec4Arg inV2)
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{
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#if defined(JPH_USE_SSE)
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return _mm_castps_si128(_mm_cmpeq_ps(inV1.mValue, inV2.mValue));
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#elif defined(JPH_USE_NEON)
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return vceqq_f32(inV1.mValue, inV2.mValue);
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#else
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return UVec4(inV1.mF32[0] == inV2.mF32[0]? 0xffffffffu : 0,
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inV1.mF32[1] == inV2.mF32[1]? 0xffffffffu : 0,
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inV1.mF32[2] == inV2.mF32[2]? 0xffffffffu : 0,
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inV1.mF32[3] == inV2.mF32[3]? 0xffffffffu : 0);
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#endif
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}
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UVec4 Vec4::sLess(Vec4Arg inV1, Vec4Arg inV2)
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{
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#if defined(JPH_USE_SSE)
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return _mm_castps_si128(_mm_cmplt_ps(inV1.mValue, inV2.mValue));
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#elif defined(JPH_USE_NEON)
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return vcltq_f32(inV1.mValue, inV2.mValue);
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#else
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return UVec4(inV1.mF32[0] < inV2.mF32[0]? 0xffffffffu : 0,
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inV1.mF32[1] < inV2.mF32[1]? 0xffffffffu : 0,
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inV1.mF32[2] < inV2.mF32[2]? 0xffffffffu : 0,
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inV1.mF32[3] < inV2.mF32[3]? 0xffffffffu : 0);
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#endif
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}
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UVec4 Vec4::sLessOrEqual(Vec4Arg inV1, Vec4Arg inV2)
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{
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#if defined(JPH_USE_SSE)
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return _mm_castps_si128(_mm_cmple_ps(inV1.mValue, inV2.mValue));
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#elif defined(JPH_USE_NEON)
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return vcleq_f32(inV1.mValue, inV2.mValue);
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#else
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return UVec4(inV1.mF32[0] <= inV2.mF32[0]? 0xffffffffu : 0,
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inV1.mF32[1] <= inV2.mF32[1]? 0xffffffffu : 0,
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inV1.mF32[2] <= inV2.mF32[2]? 0xffffffffu : 0,
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inV1.mF32[3] <= inV2.mF32[3]? 0xffffffffu : 0);
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#endif
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}
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UVec4 Vec4::sGreater(Vec4Arg inV1, Vec4Arg inV2)
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{
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#if defined(JPH_USE_SSE)
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return _mm_castps_si128(_mm_cmpgt_ps(inV1.mValue, inV2.mValue));
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#elif defined(JPH_USE_NEON)
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return vcgtq_f32(inV1.mValue, inV2.mValue);
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#else
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return UVec4(inV1.mF32[0] > inV2.mF32[0]? 0xffffffffu : 0,
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inV1.mF32[1] > inV2.mF32[1]? 0xffffffffu : 0,
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inV1.mF32[2] > inV2.mF32[2]? 0xffffffffu : 0,
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inV1.mF32[3] > inV2.mF32[3]? 0xffffffffu : 0);
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#endif
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}
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UVec4 Vec4::sGreaterOrEqual(Vec4Arg inV1, Vec4Arg inV2)
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{
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#if defined(JPH_USE_SSE)
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return _mm_castps_si128(_mm_cmpge_ps(inV1.mValue, inV2.mValue));
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#elif defined(JPH_USE_NEON)
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return vcgeq_f32(inV1.mValue, inV2.mValue);
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#else
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return UVec4(inV1.mF32[0] >= inV2.mF32[0]? 0xffffffffu : 0,
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inV1.mF32[1] >= inV2.mF32[1]? 0xffffffffu : 0,
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inV1.mF32[2] >= inV2.mF32[2]? 0xffffffffu : 0,
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inV1.mF32[3] >= inV2.mF32[3]? 0xffffffffu : 0);
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#endif
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}
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Vec4 Vec4::sFusedMultiplyAdd(Vec4Arg inMul1, Vec4Arg inMul2, Vec4Arg inAdd)
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{
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#if defined(JPH_USE_SSE)
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#ifdef JPH_USE_FMADD
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return _mm_fmadd_ps(inMul1.mValue, inMul2.mValue, inAdd.mValue);
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#else
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return _mm_add_ps(_mm_mul_ps(inMul1.mValue, inMul2.mValue), inAdd.mValue);
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#endif
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#elif defined(JPH_USE_NEON)
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return vmlaq_f32(inAdd.mValue, inMul1.mValue, inMul2.mValue);
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#else
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return Vec4(inMul1.mF32[0] * inMul2.mF32[0] + inAdd.mF32[0],
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inMul1.mF32[1] * inMul2.mF32[1] + inAdd.mF32[1],
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inMul1.mF32[2] * inMul2.mF32[2] + inAdd.mF32[2],
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inMul1.mF32[3] * inMul2.mF32[3] + inAdd.mF32[3]);
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#endif
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}
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Vec4 Vec4::sSelect(Vec4Arg inNotSet, Vec4Arg inSet, UVec4Arg inControl)
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{
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#if defined(JPH_USE_SSE4_1) && !defined(JPH_PLATFORM_WASM) // _mm_blendv_ps has problems on FireFox
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return _mm_blendv_ps(inNotSet.mValue, inSet.mValue, _mm_castsi128_ps(inControl.mValue));
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#elif defined(JPH_USE_SSE)
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__m128 is_set = _mm_castsi128_ps(_mm_srai_epi32(inControl.mValue, 31));
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return _mm_or_ps(_mm_and_ps(is_set, inSet.mValue), _mm_andnot_ps(is_set, inNotSet.mValue));
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#elif defined(JPH_USE_NEON)
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return vbslq_f32(vreinterpretq_u32_s32(vshrq_n_s32(vreinterpretq_s32_u32(inControl.mValue), 31)), inSet.mValue, inNotSet.mValue);
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#else
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Vec4 result;
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for (int i = 0; i < 4; i++)
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result.mF32[i] = (inControl.mU32[i] & 0x80000000u) ? inSet.mF32[i] : inNotSet.mF32[i];
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return result;
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#endif
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}
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Vec4 Vec4::sOr(Vec4Arg inV1, Vec4Arg inV2)
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{
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#if defined(JPH_USE_SSE)
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return _mm_or_ps(inV1.mValue, inV2.mValue);
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#elif defined(JPH_USE_NEON)
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return vreinterpretq_f32_u32(vorrq_u32(vreinterpretq_u32_f32(inV1.mValue), vreinterpretq_u32_f32(inV2.mValue)));
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#else
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return UVec4::sOr(inV1.ReinterpretAsInt(), inV2.ReinterpretAsInt()).ReinterpretAsFloat();
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#endif
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}
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Vec4 Vec4::sXor(Vec4Arg inV1, Vec4Arg inV2)
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{
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#if defined(JPH_USE_SSE)
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return _mm_xor_ps(inV1.mValue, inV2.mValue);
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#elif defined(JPH_USE_NEON)
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return vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(inV1.mValue), vreinterpretq_u32_f32(inV2.mValue)));
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#else
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return UVec4::sXor(inV1.ReinterpretAsInt(), inV2.ReinterpretAsInt()).ReinterpretAsFloat();
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#endif
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}
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Vec4 Vec4::sAnd(Vec4Arg inV1, Vec4Arg inV2)
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{
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#if defined(JPH_USE_SSE)
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return _mm_and_ps(inV1.mValue, inV2.mValue);
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#elif defined(JPH_USE_NEON)
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return vreinterpretq_f32_u32(vandq_u32(vreinterpretq_u32_f32(inV1.mValue), vreinterpretq_u32_f32(inV2.mValue)));
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#else
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return UVec4::sAnd(inV1.ReinterpretAsInt(), inV2.ReinterpretAsInt()).ReinterpretAsFloat();
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#endif
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}
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void Vec4::sSort4(Vec4 &ioValue, UVec4 &ioIndex)
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{
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// Pass 1, test 1st vs 3rd, 2nd vs 4th
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Vec4 v1 = ioValue.Swizzle<SWIZZLE_Z, SWIZZLE_W, SWIZZLE_X, SWIZZLE_Y>();
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UVec4 i1 = ioIndex.Swizzle<SWIZZLE_Z, SWIZZLE_W, SWIZZLE_X, SWIZZLE_Y>();
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UVec4 c1 = sLess(ioValue, v1).Swizzle<SWIZZLE_Z, SWIZZLE_W, SWIZZLE_Z, SWIZZLE_W>();
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ioValue = sSelect(ioValue, v1, c1);
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ioIndex = UVec4::sSelect(ioIndex, i1, c1);
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// Pass 2, test 1st vs 2nd, 3rd vs 4th
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Vec4 v2 = ioValue.Swizzle<SWIZZLE_Y, SWIZZLE_X, SWIZZLE_W, SWIZZLE_Z>();
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UVec4 i2 = ioIndex.Swizzle<SWIZZLE_Y, SWIZZLE_X, SWIZZLE_W, SWIZZLE_Z>();
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UVec4 c2 = sLess(ioValue, v2).Swizzle<SWIZZLE_Y, SWIZZLE_Y, SWIZZLE_W, SWIZZLE_W>();
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ioValue = sSelect(ioValue, v2, c2);
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ioIndex = UVec4::sSelect(ioIndex, i2, c2);
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// Pass 3, test 2nd vs 3rd component
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Vec4 v3 = ioValue.Swizzle<SWIZZLE_X, SWIZZLE_Z, SWIZZLE_Y, SWIZZLE_W>();
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UVec4 i3 = ioIndex.Swizzle<SWIZZLE_X, SWIZZLE_Z, SWIZZLE_Y, SWIZZLE_W>();
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UVec4 c3 = sLess(ioValue, v3).Swizzle<SWIZZLE_X, SWIZZLE_Z, SWIZZLE_Z, SWIZZLE_W>();
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ioValue = sSelect(ioValue, v3, c3);
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ioIndex = UVec4::sSelect(ioIndex, i3, c3);
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}
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void Vec4::sSort4Reverse(Vec4 &ioValue, UVec4 &ioIndex)
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{
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// Pass 1, test 1st vs 3rd, 2nd vs 4th
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Vec4 v1 = ioValue.Swizzle<SWIZZLE_Z, SWIZZLE_W, SWIZZLE_X, SWIZZLE_Y>();
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UVec4 i1 = ioIndex.Swizzle<SWIZZLE_Z, SWIZZLE_W, SWIZZLE_X, SWIZZLE_Y>();
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UVec4 c1 = sGreater(ioValue, v1).Swizzle<SWIZZLE_Z, SWIZZLE_W, SWIZZLE_Z, SWIZZLE_W>();
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ioValue = sSelect(ioValue, v1, c1);
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ioIndex = UVec4::sSelect(ioIndex, i1, c1);
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// Pass 2, test 1st vs 2nd, 3rd vs 4th
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Vec4 v2 = ioValue.Swizzle<SWIZZLE_Y, SWIZZLE_X, SWIZZLE_W, SWIZZLE_Z>();
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UVec4 i2 = ioIndex.Swizzle<SWIZZLE_Y, SWIZZLE_X, SWIZZLE_W, SWIZZLE_Z>();
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UVec4 c2 = sGreater(ioValue, v2).Swizzle<SWIZZLE_Y, SWIZZLE_Y, SWIZZLE_W, SWIZZLE_W>();
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ioValue = sSelect(ioValue, v2, c2);
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ioIndex = UVec4::sSelect(ioIndex, i2, c2);
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// Pass 3, test 2nd vs 3rd component
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Vec4 v3 = ioValue.Swizzle<SWIZZLE_X, SWIZZLE_Z, SWIZZLE_Y, SWIZZLE_W>();
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UVec4 i3 = ioIndex.Swizzle<SWIZZLE_X, SWIZZLE_Z, SWIZZLE_Y, SWIZZLE_W>();
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UVec4 c3 = sGreater(ioValue, v3).Swizzle<SWIZZLE_X, SWIZZLE_Z, SWIZZLE_Z, SWIZZLE_W>();
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ioValue = sSelect(ioValue, v3, c3);
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ioIndex = UVec4::sSelect(ioIndex, i3, c3);
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}
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bool Vec4::operator == (Vec4Arg inV2) const
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{
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return sEquals(*this, inV2).TestAllTrue();
|
|
}
|
|
|
|
bool Vec4::IsClose(Vec4Arg inV2, float inMaxDistSq) const
|
|
{
|
|
return (inV2 - *this).LengthSq() <= inMaxDistSq;
|
|
}
|
|
|
|
bool Vec4::IsNormalized(float inTolerance) const
|
|
{
|
|
return abs(LengthSq() - 1.0f) <= inTolerance;
|
|
}
|
|
|
|
bool Vec4::IsNaN() const
|
|
{
|
|
#if defined(JPH_USE_AVX512)
|
|
return _mm_fpclass_ps_mask(mValue, 0b10000001) != 0;
|
|
#elif defined(JPH_USE_SSE)
|
|
return _mm_movemask_ps(_mm_cmpunord_ps(mValue, mValue)) != 0;
|
|
#elif defined(JPH_USE_NEON)
|
|
uint32x4_t is_equal = vceqq_f32(mValue, mValue); // If a number is not equal to itself it's a NaN
|
|
return vaddvq_u32(vshrq_n_u32(is_equal, 31)) != 4;
|
|
#else
|
|
return isnan(mF32[0]) || isnan(mF32[1]) || isnan(mF32[2]) || isnan(mF32[3]);
|
|
#endif
|
|
}
|
|
|
|
Vec4 Vec4::operator * (Vec4Arg inV2) const
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
return _mm_mul_ps(mValue, inV2.mValue);
|
|
#elif defined(JPH_USE_NEON)
|
|
return vmulq_f32(mValue, inV2.mValue);
|
|
#else
|
|
return Vec4(mF32[0] * inV2.mF32[0],
|
|
mF32[1] * inV2.mF32[1],
|
|
mF32[2] * inV2.mF32[2],
|
|
mF32[3] * inV2.mF32[3]);
|
|
#endif
|
|
}
|
|
|
|
Vec4 Vec4::operator * (float inV2) const
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
return _mm_mul_ps(mValue, _mm_set1_ps(inV2));
|
|
#elif defined(JPH_USE_NEON)
|
|
return vmulq_n_f32(mValue, inV2);
|
|
#else
|
|
return Vec4(mF32[0] * inV2, mF32[1] * inV2, mF32[2] * inV2, mF32[3] * inV2);
|
|
#endif
|
|
}
|
|
|
|
/// Multiply vector with float
|
|
Vec4 operator * (float inV1, Vec4Arg inV2)
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
return _mm_mul_ps(_mm_set1_ps(inV1), inV2.mValue);
|
|
#elif defined(JPH_USE_NEON)
|
|
return vmulq_n_f32(inV2.mValue, inV1);
|
|
#else
|
|
return Vec4(inV1 * inV2.mF32[0],
|
|
inV1 * inV2.mF32[1],
|
|
inV1 * inV2.mF32[2],
|
|
inV1 * inV2.mF32[3]);
|
|
#endif
|
|
}
|
|
|
|
Vec4 Vec4::operator / (float inV2) const
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
return _mm_div_ps(mValue, _mm_set1_ps(inV2));
|
|
#elif defined(JPH_USE_NEON)
|
|
return vdivq_f32(mValue, vdupq_n_f32(inV2));
|
|
#else
|
|
return Vec4(mF32[0] / inV2, mF32[1] / inV2, mF32[2] / inV2, mF32[3] / inV2);
|
|
#endif
|
|
}
|
|
|
|
Vec4 &Vec4::operator *= (float inV2)
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
mValue = _mm_mul_ps(mValue, _mm_set1_ps(inV2));
|
|
#elif defined(JPH_USE_NEON)
|
|
mValue = vmulq_n_f32(mValue, inV2);
|
|
#else
|
|
for (int i = 0; i < 4; ++i)
|
|
mF32[i] *= inV2;
|
|
#endif
|
|
return *this;
|
|
}
|
|
|
|
Vec4 &Vec4::operator *= (Vec4Arg inV2)
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
mValue = _mm_mul_ps(mValue, inV2.mValue);
|
|
#elif defined(JPH_USE_NEON)
|
|
mValue = vmulq_f32(mValue, inV2.mValue);
|
|
#else
|
|
for (int i = 0; i < 4; ++i)
|
|
mF32[i] *= inV2.mF32[i];
|
|
#endif
|
|
return *this;
|
|
}
|
|
|
|
Vec4 &Vec4::operator /= (float inV2)
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
mValue = _mm_div_ps(mValue, _mm_set1_ps(inV2));
|
|
#elif defined(JPH_USE_NEON)
|
|
mValue = vdivq_f32(mValue, vdupq_n_f32(inV2));
|
|
#else
|
|
for (int i = 0; i < 4; ++i)
|
|
mF32[i] /= inV2;
|
|
#endif
|
|
return *this;
|
|
}
|
|
|
|
Vec4 Vec4::operator + (Vec4Arg inV2) const
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
return _mm_add_ps(mValue, inV2.mValue);
|
|
#elif defined(JPH_USE_NEON)
|
|
return vaddq_f32(mValue, inV2.mValue);
|
|
#else
|
|
return Vec4(mF32[0] + inV2.mF32[0],
|
|
mF32[1] + inV2.mF32[1],
|
|
mF32[2] + inV2.mF32[2],
|
|
mF32[3] + inV2.mF32[3]);
|
|
#endif
|
|
}
|
|
|
|
Vec4 &Vec4::operator += (Vec4Arg inV2)
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
mValue = _mm_add_ps(mValue, inV2.mValue);
|
|
#elif defined(JPH_USE_NEON)
|
|
mValue = vaddq_f32(mValue, inV2.mValue);
|
|
#else
|
|
for (int i = 0; i < 4; ++i)
|
|
mF32[i] += inV2.mF32[i];
|
|
#endif
|
|
return *this;
|
|
}
|
|
|
|
Vec4 Vec4::operator - () const
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
return _mm_sub_ps(_mm_setzero_ps(), mValue);
|
|
#elif defined(JPH_USE_NEON)
|
|
#ifdef JPH_CROSS_PLATFORM_DETERMINISTIC
|
|
return vsubq_f32(vdupq_n_f32(0), mValue);
|
|
#else
|
|
return vnegq_f32(mValue);
|
|
#endif
|
|
#else
|
|
#ifdef JPH_CROSS_PLATFORM_DETERMINISTIC
|
|
return Vec4(0.0f - mF32[0], 0.0f - mF32[1], 0.0f - mF32[2], 0.0f - mF32[3]);
|
|
#else
|
|
return Vec4(-mF32[0], -mF32[1], -mF32[2], -mF32[3]);
|
|
#endif
|
|
#endif
|
|
}
|
|
|
|
Vec4 Vec4::operator - (Vec4Arg inV2) const
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
return _mm_sub_ps(mValue, inV2.mValue);
|
|
#elif defined(JPH_USE_NEON)
|
|
return vsubq_f32(mValue, inV2.mValue);
|
|
#else
|
|
return Vec4(mF32[0] - inV2.mF32[0],
|
|
mF32[1] - inV2.mF32[1],
|
|
mF32[2] - inV2.mF32[2],
|
|
mF32[3] - inV2.mF32[3]);
|
|
#endif
|
|
}
|
|
|
|
Vec4 &Vec4::operator -= (Vec4Arg inV2)
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
mValue = _mm_sub_ps(mValue, inV2.mValue);
|
|
#elif defined(JPH_USE_NEON)
|
|
mValue = vsubq_f32(mValue, inV2.mValue);
|
|
#else
|
|
for (int i = 0; i < 4; ++i)
|
|
mF32[i] -= inV2.mF32[i];
|
|
#endif
|
|
return *this;
|
|
}
|
|
|
|
Vec4 Vec4::operator / (Vec4Arg inV2) const
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
return _mm_div_ps(mValue, inV2.mValue);
|
|
#elif defined(JPH_USE_NEON)
|
|
return vdivq_f32(mValue, inV2.mValue);
|
|
#else
|
|
return Vec4(mF32[0] / inV2.mF32[0],
|
|
mF32[1] / inV2.mF32[1],
|
|
mF32[2] / inV2.mF32[2],
|
|
mF32[3] / inV2.mF32[3]);
|
|
#endif
|
|
}
|
|
|
|
Vec4 Vec4::SplatX() const
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
return _mm_shuffle_ps(mValue, mValue, _MM_SHUFFLE(0, 0, 0, 0));
|
|
#elif defined(JPH_USE_NEON)
|
|
return vdupq_laneq_f32(mValue, 0);
|
|
#else
|
|
return Vec4(mF32[0], mF32[0], mF32[0], mF32[0]);
|
|
#endif
|
|
}
|
|
|
|
Vec4 Vec4::SplatY() const
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
return _mm_shuffle_ps(mValue, mValue, _MM_SHUFFLE(1, 1, 1, 1));
|
|
#elif defined(JPH_USE_NEON)
|
|
return vdupq_laneq_f32(mValue, 1);
|
|
#else
|
|
return Vec4(mF32[1], mF32[1], mF32[1], mF32[1]);
|
|
#endif
|
|
}
|
|
|
|
Vec4 Vec4::SplatZ() const
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
return _mm_shuffle_ps(mValue, mValue, _MM_SHUFFLE(2, 2, 2, 2));
|
|
#elif defined(JPH_USE_NEON)
|
|
return vdupq_laneq_f32(mValue, 2);
|
|
#else
|
|
return Vec4(mF32[2], mF32[2], mF32[2], mF32[2]);
|
|
#endif
|
|
}
|
|
|
|
Vec4 Vec4::SplatW() const
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
return _mm_shuffle_ps(mValue, mValue, _MM_SHUFFLE(3, 3, 3, 3));
|
|
#elif defined(JPH_USE_NEON)
|
|
return vdupq_laneq_f32(mValue, 3);
|
|
#else
|
|
return Vec4(mF32[3], mF32[3], mF32[3], mF32[3]);
|
|
#endif
|
|
}
|
|
|
|
Vec4 Vec4::Abs() const
|
|
{
|
|
#if defined(JPH_USE_AVX512)
|
|
return _mm_range_ps(mValue, mValue, 0b1000);
|
|
#elif defined(JPH_USE_SSE)
|
|
return _mm_max_ps(_mm_sub_ps(_mm_setzero_ps(), mValue), mValue);
|
|
#elif defined(JPH_USE_NEON)
|
|
return vabsq_f32(mValue);
|
|
#else
|
|
return Vec4(abs(mF32[0]), abs(mF32[1]), abs(mF32[2]), abs(mF32[3]));
|
|
#endif
|
|
}
|
|
|
|
Vec4 Vec4::Reciprocal() const
|
|
{
|
|
return sOne() / mValue;
|
|
}
|
|
|
|
Vec4 Vec4::DotV(Vec4Arg inV2) const
|
|
{
|
|
#if defined(JPH_USE_SSE4_1)
|
|
return _mm_dp_ps(mValue, inV2.mValue, 0xff);
|
|
#elif defined(JPH_USE_NEON)
|
|
float32x4_t mul = vmulq_f32(mValue, inV2.mValue);
|
|
return vdupq_n_f32(vaddvq_f32(mul));
|
|
#else
|
|
// Brackets placed so that the order is consistent with the vectorized version
|
|
return Vec4::sReplicate((mF32[0] * inV2.mF32[0] + mF32[1] * inV2.mF32[1]) + (mF32[2] * inV2.mF32[2] + mF32[3] * inV2.mF32[3]));
|
|
#endif
|
|
}
|
|
|
|
float Vec4::Dot(Vec4Arg inV2) const
|
|
{
|
|
#if defined(JPH_USE_SSE4_1)
|
|
return _mm_cvtss_f32(_mm_dp_ps(mValue, inV2.mValue, 0xff));
|
|
#elif defined(JPH_USE_NEON)
|
|
float32x4_t mul = vmulq_f32(mValue, inV2.mValue);
|
|
return vaddvq_f32(mul);
|
|
#else
|
|
// Brackets placed so that the order is consistent with the vectorized version
|
|
return (mF32[0] * inV2.mF32[0] + mF32[1] * inV2.mF32[1]) + (mF32[2] * inV2.mF32[2] + mF32[3] * inV2.mF32[3]);
|
|
#endif
|
|
}
|
|
|
|
float Vec4::LengthSq() const
|
|
{
|
|
#if defined(JPH_USE_SSE4_1)
|
|
return _mm_cvtss_f32(_mm_dp_ps(mValue, mValue, 0xff));
|
|
#elif defined(JPH_USE_NEON)
|
|
float32x4_t mul = vmulq_f32(mValue, mValue);
|
|
return vaddvq_f32(mul);
|
|
#else
|
|
// Brackets placed so that the order is consistent with the vectorized version
|
|
return (mF32[0] * mF32[0] + mF32[1] * mF32[1]) + (mF32[2] * mF32[2] + mF32[3] * mF32[3]);
|
|
#endif
|
|
}
|
|
|
|
float Vec4::Length() const
|
|
{
|
|
#if defined(JPH_USE_SSE4_1)
|
|
return _mm_cvtss_f32(_mm_sqrt_ss(_mm_dp_ps(mValue, mValue, 0xff)));
|
|
#elif defined(JPH_USE_NEON)
|
|
float32x4_t mul = vmulq_f32(mValue, mValue);
|
|
float32x2_t sum = vdup_n_f32(vaddvq_f32(mul));
|
|
return vget_lane_f32(vsqrt_f32(sum), 0);
|
|
#else
|
|
// Brackets placed so that the order is consistent with the vectorized version
|
|
return sqrt((mF32[0] * mF32[0] + mF32[1] * mF32[1]) + (mF32[2] * mF32[2] + mF32[3] * mF32[3]));
|
|
#endif
|
|
}
|
|
|
|
Vec4 Vec4::Sqrt() const
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
return _mm_sqrt_ps(mValue);
|
|
#elif defined(JPH_USE_NEON)
|
|
return vsqrtq_f32(mValue);
|
|
#else
|
|
return Vec4(sqrt(mF32[0]), sqrt(mF32[1]), sqrt(mF32[2]), sqrt(mF32[3]));
|
|
#endif
|
|
}
|
|
|
|
|
|
Vec4 Vec4::GetSign() const
|
|
{
|
|
#if defined(JPH_USE_AVX512)
|
|
return _mm_fixupimm_ps(mValue, mValue, _mm_set1_epi32(0xA9A90A00), 0);
|
|
#elif defined(JPH_USE_SSE)
|
|
Type minus_one = _mm_set1_ps(-1.0f);
|
|
Type one = _mm_set1_ps(1.0f);
|
|
return _mm_or_ps(_mm_and_ps(mValue, minus_one), one);
|
|
#elif defined(JPH_USE_NEON)
|
|
Type minus_one = vdupq_n_f32(-1.0f);
|
|
Type one = vdupq_n_f32(1.0f);
|
|
return vreinterpretq_f32_u32(vorrq_u32(vandq_u32(vreinterpretq_u32_f32(mValue), vreinterpretq_u32_f32(minus_one)), vreinterpretq_u32_f32(one)));
|
|
#else
|
|
return Vec4(std::signbit(mF32[0])? -1.0f : 1.0f,
|
|
std::signbit(mF32[1])? -1.0f : 1.0f,
|
|
std::signbit(mF32[2])? -1.0f : 1.0f,
|
|
std::signbit(mF32[3])? -1.0f : 1.0f);
|
|
#endif
|
|
}
|
|
|
|
Vec4 Vec4::Normalized() const
|
|
{
|
|
#if defined(JPH_USE_SSE4_1)
|
|
return _mm_div_ps(mValue, _mm_sqrt_ps(_mm_dp_ps(mValue, mValue, 0xff)));
|
|
#elif defined(JPH_USE_NEON)
|
|
float32x4_t mul = vmulq_f32(mValue, mValue);
|
|
float32x4_t sum = vdupq_n_f32(vaddvq_f32(mul));
|
|
return vdivq_f32(mValue, vsqrtq_f32(sum));
|
|
#else
|
|
return *this / Length();
|
|
#endif
|
|
}
|
|
|
|
void Vec4::StoreFloat4(Float4 *outV) const
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
_mm_storeu_ps(&outV->x, mValue);
|
|
#elif defined(JPH_USE_NEON)
|
|
vst1q_f32(&outV->x, mValue);
|
|
#else
|
|
for (int i = 0; i < 4; ++i)
|
|
(&outV->x)[i] = mF32[i];
|
|
#endif
|
|
}
|
|
|
|
UVec4 Vec4::ToInt() const
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
return _mm_cvttps_epi32(mValue);
|
|
#elif defined(JPH_USE_NEON)
|
|
return vcvtq_u32_f32(mValue);
|
|
#else
|
|
return UVec4(uint32(mF32[0]), uint32(mF32[1]), uint32(mF32[2]), uint32(mF32[3]));
|
|
#endif
|
|
}
|
|
|
|
UVec4 Vec4::ReinterpretAsInt() const
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
return UVec4(_mm_castps_si128(mValue));
|
|
#elif defined(JPH_USE_NEON)
|
|
return vreinterpretq_u32_f32(mValue);
|
|
#else
|
|
return *reinterpret_cast<const UVec4 *>(this);
|
|
#endif
|
|
}
|
|
|
|
int Vec4::GetSignBits() const
|
|
{
|
|
#if defined(JPH_USE_SSE)
|
|
return _mm_movemask_ps(mValue);
|
|
#elif defined(JPH_USE_NEON)
|
|
int32x4_t shift = JPH_NEON_INT32x4(0, 1, 2, 3);
|
|
return vaddvq_u32(vshlq_u32(vshrq_n_u32(vreinterpretq_u32_f32(mValue), 31), shift));
|
|
#else
|
|
return (std::signbit(mF32[0])? 1 : 0) | (std::signbit(mF32[1])? 2 : 0) | (std::signbit(mF32[2])? 4 : 0) | (std::signbit(mF32[3])? 8 : 0);
|
|
#endif
|
|
}
|
|
|
|
float Vec4::ReduceMin() const
|
|
{
|
|
Vec4 v = sMin(mValue, Swizzle<SWIZZLE_Y, SWIZZLE_UNUSED, SWIZZLE_W, SWIZZLE_UNUSED>());
|
|
v = sMin(v, v.Swizzle<SWIZZLE_Z, SWIZZLE_UNUSED, SWIZZLE_UNUSED, SWIZZLE_UNUSED>());
|
|
return v.GetX();
|
|
}
|
|
|
|
float Vec4::ReduceMax() const
|
|
{
|
|
Vec4 v = sMax(mValue, Swizzle<SWIZZLE_Y, SWIZZLE_UNUSED, SWIZZLE_W, SWIZZLE_UNUSED>());
|
|
v = sMax(v, v.Swizzle<SWIZZLE_Z, SWIZZLE_UNUSED, SWIZZLE_UNUSED, SWIZZLE_UNUSED>());
|
|
return v.GetX();
|
|
}
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void Vec4::SinCos(Vec4 &outSin, Vec4 &outCos) const
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{
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// Implementation based on sinf.c from the cephes library, combines sinf and cosf in a single function, changes octants to quadrants and vectorizes it
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// Original implementation by Stephen L. Moshier (See: http://www.moshier.net/)
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// Make argument positive and remember sign for sin only since cos is symmetric around x (highest bit of a float is the sign bit)
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UVec4 sin_sign = UVec4::sAnd(ReinterpretAsInt(), UVec4::sReplicate(0x80000000U));
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Vec4 x = Vec4::sXor(*this, sin_sign.ReinterpretAsFloat());
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// x / (PI / 2) rounded to nearest int gives us the quadrant closest to x
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UVec4 quadrant = (0.6366197723675814f * x + Vec4::sReplicate(0.5f)).ToInt();
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// Make x relative to the closest quadrant.
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// This does x = x - quadrant * PI / 2 using a two step Cody-Waite argument reduction.
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// This improves the accuracy of the result by avoiding loss of significant bits in the subtraction.
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// We start with x = x - quadrant * PI / 2, PI / 2 in hexadecimal notation is 0x3fc90fdb, we remove the lowest 16 bits to
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// get 0x3fc90000 (= 1.5703125) this means we can now multiply with a number of up to 2^16 without losing any bits.
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// This leaves us with: x = (x - quadrant * 1.5703125) - quadrant * (PI / 2 - 1.5703125).
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// PI / 2 - 1.5703125 in hexadecimal is 0x39fdaa22, stripping the lowest 12 bits we get 0x39fda000 (= 0.0004837512969970703125)
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// This leaves uw with: x = ((x - quadrant * 1.5703125) - quadrant * 0.0004837512969970703125) - quadrant * (PI / 2 - 1.5703125 - 0.0004837512969970703125)
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// See: https://stackoverflow.com/questions/42455143/sine-cosine-modular-extended-precision-arithmetic
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// After this we have x in the range [-PI / 4, PI / 4].
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Vec4 float_quadrant = quadrant.ToFloat();
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x = ((x - float_quadrant * 1.5703125f) - float_quadrant * 0.0004837512969970703125f) - float_quadrant * 7.549789948768648e-8f;
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// Calculate x2 = x^2
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Vec4 x2 = x * x;
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// Taylor expansion:
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// Cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8! + ... = (((x2/8!- 1/6!) * x2 + 1/4!) * x2 - 1/2!) * x2 + 1
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Vec4 taylor_cos = ((2.443315711809948e-5f * x2 - Vec4::sReplicate(1.388731625493765e-3f)) * x2 + Vec4::sReplicate(4.166664568298827e-2f)) * x2 * x2 - 0.5f * x2 + Vec4::sOne();
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// Sin(x) = x - x^3/3! + x^5/5! - x^7/7! + ... = ((-x2/7! + 1/5!) * x2 - 1/3!) * x2 * x + x
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Vec4 taylor_sin = ((-1.9515295891e-4f * x2 + Vec4::sReplicate(8.3321608736e-3f)) * x2 - Vec4::sReplicate(1.6666654611e-1f)) * x2 * x + x;
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// The lowest 2 bits of quadrant indicate the quadrant that we are in.
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// Let x be the original input value and x' our value that has been mapped to the range [-PI / 4, PI / 4].
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// since cos(x) = sin(x - PI / 2) and since we want to use the Taylor expansion as close as possible to 0,
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// we can alternate between using the Taylor expansion for sin and cos according to the following table:
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//
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// quadrant sin(x) cos(x)
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// XXX00b sin(x') cos(x')
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// XXX01b cos(x') -sin(x')
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// XXX10b -sin(x') -cos(x')
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// XXX11b -cos(x') sin(x')
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//
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// So: sin_sign = bit2, cos_sign = bit1 ^ bit2, bit1 determines if we use sin or cos Taylor expansion
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UVec4 bit1 = quadrant.LogicalShiftLeft<31>();
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UVec4 bit2 = UVec4::sAnd(quadrant.LogicalShiftLeft<30>(), UVec4::sReplicate(0x80000000U));
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// Select which one of the results is sin and which one is cos
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Vec4 s = Vec4::sSelect(taylor_sin, taylor_cos, bit1);
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Vec4 c = Vec4::sSelect(taylor_cos, taylor_sin, bit1);
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// Update the signs
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sin_sign = UVec4::sXor(sin_sign, bit2);
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UVec4 cos_sign = UVec4::sXor(bit1, bit2);
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// Correct the signs
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outSin = Vec4::sXor(s, sin_sign.ReinterpretAsFloat());
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outCos = Vec4::sXor(c, cos_sign.ReinterpretAsFloat());
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}
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Vec4 Vec4::Tan() const
|
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{
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// Implementation based on tanf.c from the cephes library, see Vec4::SinCos for further details
|
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// Original implementation by Stephen L. Moshier (See: http://www.moshier.net/)
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// Make argument positive
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UVec4 tan_sign = UVec4::sAnd(ReinterpretAsInt(), UVec4::sReplicate(0x80000000U));
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Vec4 x = Vec4::sXor(*this, tan_sign.ReinterpretAsFloat());
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|
// x / (PI / 2) rounded to nearest int gives us the quadrant closest to x
|
|
UVec4 quadrant = (0.6366197723675814f * x + Vec4::sReplicate(0.5f)).ToInt();
|
|
|
|
// Remap x to range [-PI / 4, PI / 4], see Vec4::SinCos
|
|
Vec4 float_quadrant = quadrant.ToFloat();
|
|
x = ((x - float_quadrant * 1.5703125f) - float_quadrant * 0.0004837512969970703125f) - float_quadrant * 7.549789948768648e-8f;
|
|
|
|
// Calculate x2 = x^2
|
|
Vec4 x2 = x * x;
|
|
|
|
// Roughly equivalent to the Taylor expansion:
|
|
// Tan(x) = x + x^3/3 + 2*x^5/15 + 17*x^7/315 + 62*x^9/2835 + ...
|
|
Vec4 tan =
|
|
(((((9.38540185543e-3f * x2 + Vec4::sReplicate(3.11992232697e-3f)) * x2 + Vec4::sReplicate(2.44301354525e-2f)) * x2
|
|
+ Vec4::sReplicate(5.34112807005e-2f)) * x2 + Vec4::sReplicate(1.33387994085e-1f)) * x2 + Vec4::sReplicate(3.33331568548e-1f)) * x2 * x + x;
|
|
|
|
// For the 2nd and 4th quadrant we need to invert the value
|
|
UVec4 bit1 = quadrant.LogicalShiftLeft<31>();
|
|
tan = Vec4::sSelect(tan, Vec4::sReplicate(-1.0f) / (tan JPH_IF_FLOATING_POINT_EXCEPTIONS_ENABLED(+ Vec4::sReplicate(FLT_MIN))), bit1); // Add small epsilon to prevent div by zero, works because tan is always positive
|
|
|
|
// Put the sign back
|
|
return Vec4::sXor(tan, tan_sign.ReinterpretAsFloat());
|
|
}
|
|
|
|
Vec4 Vec4::ASin() const
|
|
{
|
|
// Implementation based on asinf.c from the cephes library
|
|
// Original implementation by Stephen L. Moshier (See: http://www.moshier.net/)
|
|
|
|
// Make argument positive
|
|
UVec4 asin_sign = UVec4::sAnd(ReinterpretAsInt(), UVec4::sReplicate(0x80000000U));
|
|
Vec4 a = Vec4::sXor(*this, asin_sign.ReinterpretAsFloat());
|
|
|
|
// ASin is not defined outside the range [-1, 1] but it often happens that a value is slightly above 1 so we just clamp here
|
|
a = Vec4::sMin(a, Vec4::sOne());
|
|
|
|
// When |x| <= 0.5 we use the asin approximation as is
|
|
Vec4 z1 = a * a;
|
|
Vec4 x1 = a;
|
|
|
|
// When |x| > 0.5 we use the identity asin(x) = PI / 2 - 2 * asin(sqrt((1 - x) / 2))
|
|
Vec4 z2 = 0.5f * (Vec4::sOne() - a);
|
|
Vec4 x2 = z2.Sqrt();
|
|
|
|
// Select which of the two situations we have
|
|
UVec4 greater = Vec4::sGreater(a, Vec4::sReplicate(0.5f));
|
|
Vec4 z = Vec4::sSelect(z1, z2, greater);
|
|
Vec4 x = Vec4::sSelect(x1, x2, greater);
|
|
|
|
// Polynomial approximation of asin
|
|
z = ((((4.2163199048e-2f * z + Vec4::sReplicate(2.4181311049e-2f)) * z + Vec4::sReplicate(4.5470025998e-2f)) * z + Vec4::sReplicate(7.4953002686e-2f)) * z + Vec4::sReplicate(1.6666752422e-1f)) * z * x + x;
|
|
|
|
// If |x| > 0.5 we need to apply the remainder of the identity above
|
|
z = Vec4::sSelect(z, Vec4::sReplicate(0.5f * JPH_PI) - (z + z), greater);
|
|
|
|
// Put the sign back
|
|
return Vec4::sXor(z, asin_sign.ReinterpretAsFloat());
|
|
}
|
|
|
|
Vec4 Vec4::ACos() const
|
|
{
|
|
// Not the most accurate, but simple
|
|
return Vec4::sReplicate(0.5f * JPH_PI) - ASin();
|
|
}
|
|
|
|
Vec4 Vec4::ATan() const
|
|
{
|
|
// Implementation based on atanf.c from the cephes library
|
|
// Original implementation by Stephen L. Moshier (See: http://www.moshier.net/)
|
|
|
|
// Make argument positive
|
|
UVec4 atan_sign = UVec4::sAnd(ReinterpretAsInt(), UVec4::sReplicate(0x80000000U));
|
|
Vec4 x = Vec4::sXor(*this, atan_sign.ReinterpretAsFloat());
|
|
Vec4 y = Vec4::sZero();
|
|
|
|
// If x > Tan(PI / 8)
|
|
UVec4 greater1 = Vec4::sGreater(x, Vec4::sReplicate(0.4142135623730950f));
|
|
Vec4 x1 = (x - Vec4::sOne()) / (x + Vec4::sOne());
|
|
|
|
// If x > Tan(3 * PI / 8)
|
|
UVec4 greater2 = Vec4::sGreater(x, Vec4::sReplicate(2.414213562373095f));
|
|
Vec4 x2 = Vec4::sReplicate(-1.0f) / (x JPH_IF_FLOATING_POINT_EXCEPTIONS_ENABLED(+ Vec4::sReplicate(FLT_MIN))); // Add small epsilon to prevent div by zero, works because x is always positive
|
|
|
|
// Apply first if
|
|
x = Vec4::sSelect(x, x1, greater1);
|
|
y = Vec4::sSelect(y, Vec4::sReplicate(0.25f * JPH_PI), greater1);
|
|
|
|
// Apply second if
|
|
x = Vec4::sSelect(x, x2, greater2);
|
|
y = Vec4::sSelect(y, Vec4::sReplicate(0.5f * JPH_PI), greater2);
|
|
|
|
// Polynomial approximation
|
|
Vec4 z = x * x;
|
|
y += (((8.05374449538e-2f * z - Vec4::sReplicate(1.38776856032e-1f)) * z + Vec4::sReplicate(1.99777106478e-1f)) * z - Vec4::sReplicate(3.33329491539e-1f)) * z * x + x;
|
|
|
|
// Put the sign back
|
|
return Vec4::sXor(y, atan_sign.ReinterpretAsFloat());
|
|
}
|
|
|
|
Vec4 Vec4::sATan2(Vec4Arg inY, Vec4Arg inX)
|
|
{
|
|
UVec4 sign_mask = UVec4::sReplicate(0x80000000U);
|
|
|
|
// Determine absolute value and sign of y
|
|
UVec4 y_sign = UVec4::sAnd(inY.ReinterpretAsInt(), sign_mask);
|
|
Vec4 y_abs = Vec4::sXor(inY, y_sign.ReinterpretAsFloat());
|
|
|
|
// Determine absolute value and sign of x
|
|
UVec4 x_sign = UVec4::sAnd(inX.ReinterpretAsInt(), sign_mask);
|
|
Vec4 x_abs = Vec4::sXor(inX, x_sign.ReinterpretAsFloat());
|
|
|
|
// Always divide smallest / largest to avoid dividing by zero
|
|
UVec4 x_is_numerator = Vec4::sLess(x_abs, y_abs);
|
|
Vec4 numerator = Vec4::sSelect(y_abs, x_abs, x_is_numerator);
|
|
Vec4 denominator = Vec4::sSelect(x_abs, y_abs, x_is_numerator);
|
|
Vec4 atan = (numerator / denominator).ATan();
|
|
|
|
// If we calculated x / y instead of y / x the result is PI / 2 - result (note that this is true because we know the result is positive because the input was positive)
|
|
atan = Vec4::sSelect(atan, Vec4::sReplicate(0.5f * JPH_PI) - atan, x_is_numerator);
|
|
|
|
// Now we need to map to the correct quadrant
|
|
// x_sign y_sign result
|
|
// +1 +1 atan
|
|
// -1 +1 -atan + PI
|
|
// -1 -1 atan - PI
|
|
// +1 -1 -atan
|
|
// This can be written as: x_sign * y_sign * (atan - (x_sign < 0? PI : 0))
|
|
atan -= Vec4::sAnd(x_sign.ArithmeticShiftRight<31>().ReinterpretAsFloat(), Vec4::sReplicate(JPH_PI));
|
|
atan = Vec4::sXor(atan, UVec4::sXor(x_sign, y_sign).ReinterpretAsFloat());
|
|
return atan;
|
|
}
|
|
|
|
JPH_NAMESPACE_END
|