// Jolt Physics Library (https://github.com/jrouwe/JoltPhysics) // SPDX-FileCopyrightText: 2021 Jorrit Rouwe // SPDX-License-Identifier: MIT #include #include #include JPH_NAMESPACE_BEGIN // Constructor Vec4::Vec4(Vec3Arg inRHS) : mValue(inRHS.mValue) { } Vec4::Vec4(Vec3Arg inRHS, float inW) { #if defined(JPH_USE_SSE4_1) mValue = _mm_blend_ps(inRHS.mValue, _mm_set1_ps(inW), 8); #elif defined(JPH_USE_NEON) mValue = vsetq_lane_f32(inW, inRHS.mValue, 3); #else for (int i = 0; i < 3; i++) mF32[i] = inRHS.mF32[i]; mF32[3] = inW; #endif } Vec4::Vec4(float inX, float inY, float inZ, float inW) { #if defined(JPH_USE_SSE) mValue = _mm_set_ps(inW, inZ, inY, inX); #elif defined(JPH_USE_NEON) uint32x2_t xy = vcreate_u32(static_cast(BitCast(inX)) | (static_cast(BitCast(inY)) << 32)); uint32x2_t zw = vcreate_u32(static_cast(BitCast(inZ)) | (static_cast(BitCast(inW)) << 32)); mValue = vreinterpretq_f32_u32(vcombine_u32(xy, zw)); #else mF32[0] = inX; mF32[1] = inY; mF32[2] = inZ; mF32[3] = inW; #endif } template Vec4 Vec4::Swizzle() const { static_assert(SwizzleX <= 3, "SwizzleX template parameter out of range"); static_assert(SwizzleY <= 3, "SwizzleY template parameter out of range"); static_assert(SwizzleZ <= 3, "SwizzleZ template parameter out of range"); static_assert(SwizzleW <= 3, "SwizzleW template parameter out of range"); #if defined(JPH_USE_SSE) return _mm_shuffle_ps(mValue, mValue, _MM_SHUFFLE(SwizzleW, SwizzleZ, SwizzleY, SwizzleX)); #elif defined(JPH_USE_NEON) return JPH_NEON_SHUFFLE_F32x4(mValue, mValue, SwizzleX, SwizzleY, SwizzleZ, SwizzleW); #else return Vec4(mF32[SwizzleX], mF32[SwizzleY], mF32[SwizzleZ], mF32[SwizzleW]); #endif } Vec4 Vec4::sZero() { #if defined(JPH_USE_SSE) return _mm_setzero_ps(); #elif defined(JPH_USE_NEON) return vdupq_n_f32(0); #else return Vec4(0, 0, 0, 0); #endif } Vec4 Vec4::sReplicate(float inV) { #if defined(JPH_USE_SSE) return _mm_set1_ps(inV); #elif defined(JPH_USE_NEON) return vdupq_n_f32(inV); #else return Vec4(inV, inV, inV, inV); #endif } Vec4 Vec4::sOne() { return sReplicate(1.0f); } Vec4 Vec4::sNaN() { return sReplicate(numeric_limits::quiet_NaN()); } Vec4 Vec4::sLoadFloat4(const Float4 *inV) { #if defined(JPH_USE_SSE) return _mm_loadu_ps(&inV->x); #elif defined(JPH_USE_NEON) return vld1q_f32(&inV->x); #else return Vec4(inV->x, inV->y, inV->z, inV->w); #endif } Vec4 Vec4::sLoadFloat4Aligned(const Float4 *inV) { #if defined(JPH_USE_SSE) return _mm_load_ps(&inV->x); #elif defined(JPH_USE_NEON) return vld1q_f32(&inV->x); #else return Vec4(inV->x, inV->y, inV->z, inV->w); #endif } template Vec4 Vec4::sGatherFloat4(const float *inBase, UVec4Arg inOffsets) { #if defined(JPH_USE_SSE) #ifdef JPH_USE_AVX2 return _mm_i32gather_ps(inBase, inOffsets.mValue, Scale); #else const uint8 *base = reinterpret_cast(inBase); Type x = _mm_load_ss(reinterpret_cast(base + inOffsets.GetX() * Scale)); Type y = _mm_load_ss(reinterpret_cast(base + inOffsets.GetY() * Scale)); Type xy = _mm_unpacklo_ps(x, y); Type z = _mm_load_ss(reinterpret_cast(base + inOffsets.GetZ() * Scale)); Type w = _mm_load_ss(reinterpret_cast(base + inOffsets.GetW() * Scale)); Type zw = _mm_unpacklo_ps(z, w); return _mm_movelh_ps(xy, zw); #endif #else const uint8 *base = reinterpret_cast(inBase); float x = *reinterpret_cast(base + inOffsets.GetX() * Scale); float y = *reinterpret_cast(base + inOffsets.GetY() * Scale); float z = *reinterpret_cast(base + inOffsets.GetZ() * Scale); float w = *reinterpret_cast(base + inOffsets.GetW() * Scale); return Vec4(x, y, z, w); #endif } Vec4 Vec4::sMin(Vec4Arg inV1, Vec4Arg inV2) { #if defined(JPH_USE_SSE) return _mm_min_ps(inV1.mValue, inV2.mValue); #elif defined(JPH_USE_NEON) return vminq_f32(inV1.mValue, inV2.mValue); #else return Vec4(min(inV1.mF32[0], inV2.mF32[0]), min(inV1.mF32[1], inV2.mF32[1]), min(inV1.mF32[2], inV2.mF32[2]), min(inV1.mF32[3], inV2.mF32[3])); #endif } Vec4 Vec4::sMax(Vec4Arg inV1, Vec4Arg inV2) { #if defined(JPH_USE_SSE) return _mm_max_ps(inV1.mValue, inV2.mValue); #elif defined(JPH_USE_NEON) return vmaxq_f32(inV1.mValue, inV2.mValue); #else return Vec4(max(inV1.mF32[0], inV2.mF32[0]), max(inV1.mF32[1], inV2.mF32[1]), max(inV1.mF32[2], inV2.mF32[2]), max(inV1.mF32[3], inV2.mF32[3])); #endif } UVec4 Vec4::sEquals(Vec4Arg inV1, Vec4Arg inV2) { #if defined(JPH_USE_SSE) return _mm_castps_si128(_mm_cmpeq_ps(inV1.mValue, inV2.mValue)); #elif defined(JPH_USE_NEON) return vceqq_f32(inV1.mValue, inV2.mValue); #else return UVec4(inV1.mF32[0] == inV2.mF32[0]? 0xffffffffu : 0, inV1.mF32[1] == inV2.mF32[1]? 0xffffffffu : 0, inV1.mF32[2] == inV2.mF32[2]? 0xffffffffu : 0, inV1.mF32[3] == inV2.mF32[3]? 0xffffffffu : 0); #endif } UVec4 Vec4::sLess(Vec4Arg inV1, Vec4Arg inV2) { #if defined(JPH_USE_SSE) return _mm_castps_si128(_mm_cmplt_ps(inV1.mValue, inV2.mValue)); #elif defined(JPH_USE_NEON) return vcltq_f32(inV1.mValue, inV2.mValue); #else return UVec4(inV1.mF32[0] < inV2.mF32[0]? 0xffffffffu : 0, inV1.mF32[1] < inV2.mF32[1]? 0xffffffffu : 0, inV1.mF32[2] < inV2.mF32[2]? 0xffffffffu : 0, inV1.mF32[3] < inV2.mF32[3]? 0xffffffffu : 0); #endif } UVec4 Vec4::sLessOrEqual(Vec4Arg inV1, Vec4Arg inV2) { #if defined(JPH_USE_SSE) return _mm_castps_si128(_mm_cmple_ps(inV1.mValue, inV2.mValue)); #elif defined(JPH_USE_NEON) return vcleq_f32(inV1.mValue, inV2.mValue); #else return UVec4(inV1.mF32[0] <= inV2.mF32[0]? 0xffffffffu : 0, inV1.mF32[1] <= inV2.mF32[1]? 0xffffffffu : 0, inV1.mF32[2] <= inV2.mF32[2]? 0xffffffffu : 0, inV1.mF32[3] <= inV2.mF32[3]? 0xffffffffu : 0); #endif } UVec4 Vec4::sGreater(Vec4Arg inV1, Vec4Arg inV2) { #if defined(JPH_USE_SSE) return _mm_castps_si128(_mm_cmpgt_ps(inV1.mValue, inV2.mValue)); #elif defined(JPH_USE_NEON) return vcgtq_f32(inV1.mValue, inV2.mValue); #else return UVec4(inV1.mF32[0] > inV2.mF32[0]? 0xffffffffu : 0, inV1.mF32[1] > inV2.mF32[1]? 0xffffffffu : 0, inV1.mF32[2] > inV2.mF32[2]? 0xffffffffu : 0, inV1.mF32[3] > inV2.mF32[3]? 0xffffffffu : 0); #endif } UVec4 Vec4::sGreaterOrEqual(Vec4Arg inV1, Vec4Arg inV2) { #if defined(JPH_USE_SSE) return _mm_castps_si128(_mm_cmpge_ps(inV1.mValue, inV2.mValue)); #elif defined(JPH_USE_NEON) return vcgeq_f32(inV1.mValue, inV2.mValue); #else return UVec4(inV1.mF32[0] >= inV2.mF32[0]? 0xffffffffu : 0, inV1.mF32[1] >= inV2.mF32[1]? 0xffffffffu : 0, inV1.mF32[2] >= inV2.mF32[2]? 0xffffffffu : 0, inV1.mF32[3] >= inV2.mF32[3]? 0xffffffffu : 0); #endif } Vec4 Vec4::sFusedMultiplyAdd(Vec4Arg inMul1, Vec4Arg inMul2, Vec4Arg inAdd) { #if defined(JPH_USE_SSE) #ifdef JPH_USE_FMADD return _mm_fmadd_ps(inMul1.mValue, inMul2.mValue, inAdd.mValue); #else return _mm_add_ps(_mm_mul_ps(inMul1.mValue, inMul2.mValue), inAdd.mValue); #endif #elif defined(JPH_USE_NEON) return vmlaq_f32(inAdd.mValue, inMul1.mValue, inMul2.mValue); #else return Vec4(inMul1.mF32[0] * inMul2.mF32[0] + inAdd.mF32[0], inMul1.mF32[1] * inMul2.mF32[1] + inAdd.mF32[1], inMul1.mF32[2] * inMul2.mF32[2] + inAdd.mF32[2], inMul1.mF32[3] * inMul2.mF32[3] + inAdd.mF32[3]); #endif } Vec4 Vec4::sSelect(Vec4Arg inNotSet, Vec4Arg inSet, UVec4Arg inControl) { #if defined(JPH_USE_SSE4_1) && !defined(JPH_PLATFORM_WASM) // _mm_blendv_ps has problems on FireFox return _mm_blendv_ps(inNotSet.mValue, inSet.mValue, _mm_castsi128_ps(inControl.mValue)); #elif defined(JPH_USE_SSE) __m128 is_set = _mm_castsi128_ps(_mm_srai_epi32(inControl.mValue, 31)); return _mm_or_ps(_mm_and_ps(is_set, inSet.mValue), _mm_andnot_ps(is_set, inNotSet.mValue)); #elif defined(JPH_USE_NEON) return vbslq_f32(vreinterpretq_u32_s32(vshrq_n_s32(vreinterpretq_s32_u32(inControl.mValue), 31)), inSet.mValue, inNotSet.mValue); #else Vec4 result; for (int i = 0; i < 4; i++) result.mF32[i] = (inControl.mU32[i] & 0x80000000u) ? inSet.mF32[i] : inNotSet.mF32[i]; return result; #endif } Vec4 Vec4::sOr(Vec4Arg inV1, Vec4Arg inV2) { #if defined(JPH_USE_SSE) return _mm_or_ps(inV1.mValue, inV2.mValue); #elif defined(JPH_USE_NEON) return vreinterpretq_f32_u32(vorrq_u32(vreinterpretq_u32_f32(inV1.mValue), vreinterpretq_u32_f32(inV2.mValue))); #else return UVec4::sOr(inV1.ReinterpretAsInt(), inV2.ReinterpretAsInt()).ReinterpretAsFloat(); #endif } Vec4 Vec4::sXor(Vec4Arg inV1, Vec4Arg inV2) { #if defined(JPH_USE_SSE) return _mm_xor_ps(inV1.mValue, inV2.mValue); #elif defined(JPH_USE_NEON) return vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(inV1.mValue), vreinterpretq_u32_f32(inV2.mValue))); #else return UVec4::sXor(inV1.ReinterpretAsInt(), inV2.ReinterpretAsInt()).ReinterpretAsFloat(); #endif } Vec4 Vec4::sAnd(Vec4Arg inV1, Vec4Arg inV2) { #if defined(JPH_USE_SSE) return _mm_and_ps(inV1.mValue, inV2.mValue); #elif defined(JPH_USE_NEON) return vreinterpretq_f32_u32(vandq_u32(vreinterpretq_u32_f32(inV1.mValue), vreinterpretq_u32_f32(inV2.mValue))); #else return UVec4::sAnd(inV1.ReinterpretAsInt(), inV2.ReinterpretAsInt()).ReinterpretAsFloat(); #endif } void Vec4::sSort4(Vec4 &ioValue, UVec4 &ioIndex) { // Pass 1, test 1st vs 3rd, 2nd vs 4th Vec4 v1 = ioValue.Swizzle(); UVec4 i1 = ioIndex.Swizzle(); UVec4 c1 = sLess(ioValue, v1).Swizzle(); ioValue = sSelect(ioValue, v1, c1); ioIndex = UVec4::sSelect(ioIndex, i1, c1); // Pass 2, test 1st vs 2nd, 3rd vs 4th Vec4 v2 = ioValue.Swizzle(); UVec4 i2 = ioIndex.Swizzle(); UVec4 c2 = sLess(ioValue, v2).Swizzle(); ioValue = sSelect(ioValue, v2, c2); ioIndex = UVec4::sSelect(ioIndex, i2, c2); // Pass 3, test 2nd vs 3rd component Vec4 v3 = ioValue.Swizzle(); UVec4 i3 = ioIndex.Swizzle(); UVec4 c3 = sLess(ioValue, v3).Swizzle(); ioValue = sSelect(ioValue, v3, c3); ioIndex = UVec4::sSelect(ioIndex, i3, c3); } void Vec4::sSort4Reverse(Vec4 &ioValue, UVec4 &ioIndex) { // Pass 1, test 1st vs 3rd, 2nd vs 4th Vec4 v1 = ioValue.Swizzle(); UVec4 i1 = ioIndex.Swizzle(); UVec4 c1 = sGreater(ioValue, v1).Swizzle(); ioValue = sSelect(ioValue, v1, c1); ioIndex = UVec4::sSelect(ioIndex, i1, c1); // Pass 2, test 1st vs 2nd, 3rd vs 4th Vec4 v2 = ioValue.Swizzle(); UVec4 i2 = ioIndex.Swizzle(); UVec4 c2 = sGreater(ioValue, v2).Swizzle(); ioValue = sSelect(ioValue, v2, c2); ioIndex = UVec4::sSelect(ioIndex, i2, c2); // Pass 3, test 2nd vs 3rd component Vec4 v3 = ioValue.Swizzle(); UVec4 i3 = ioIndex.Swizzle(); UVec4 c3 = sGreater(ioValue, v3).Swizzle(); ioValue = sSelect(ioValue, v3, c3); ioIndex = UVec4::sSelect(ioIndex, i3, c3); } bool Vec4::operator == (Vec4Arg inV2) const { 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(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()); v = sMin(v, v.Swizzle()); return v.GetX(); } float Vec4::ReduceMax() const { Vec4 v = sMax(mValue, Swizzle()); v = sMax(v, v.Swizzle()); return v.GetX(); } void Vec4::SinCos(Vec4 &outSin, Vec4 &outCos) const { // Implementation based on sinf.c from the cephes library, combines sinf and cosf in a single function, changes octants to quadrants and vectorizes it // Original implementation by Stephen L. Moshier (See: http://www.moshier.net/) // Make argument positive and remember sign for sin only since cos is symmetric around x (highest bit of a float is the sign bit) UVec4 sin_sign = UVec4::sAnd(ReinterpretAsInt(), UVec4::sReplicate(0x80000000U)); Vec4 x = Vec4::sXor(*this, sin_sign.ReinterpretAsFloat()); // x / (PI / 2) rounded to nearest int gives us the quadrant closest to x UVec4 quadrant = (0.6366197723675814f * x + Vec4::sReplicate(0.5f)).ToInt(); // Make x relative to the closest quadrant. // This does x = x - quadrant * PI / 2 using a two step Cody-Waite argument reduction. // This improves the accuracy of the result by avoiding loss of significant bits in the subtraction. // We start with x = x - quadrant * PI / 2, PI / 2 in hexadecimal notation is 0x3fc90fdb, we remove the lowest 16 bits to // get 0x3fc90000 (= 1.5703125) this means we can now multiply with a number of up to 2^16 without losing any bits. // This leaves us with: x = (x - quadrant * 1.5703125) - quadrant * (PI / 2 - 1.5703125). // PI / 2 - 1.5703125 in hexadecimal is 0x39fdaa22, stripping the lowest 12 bits we get 0x39fda000 (= 0.0004837512969970703125) // This leaves uw with: x = ((x - quadrant * 1.5703125) - quadrant * 0.0004837512969970703125) - quadrant * (PI / 2 - 1.5703125 - 0.0004837512969970703125) // See: https://stackoverflow.com/questions/42455143/sine-cosine-modular-extended-precision-arithmetic // After this we have x in the range [-PI / 4, PI / 4]. 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; // Taylor expansion: // 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 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(); // Sin(x) = x - x^3/3! + x^5/5! - x^7/7! + ... = ((-x2/7! + 1/5!) * x2 - 1/3!) * x2 * x + x Vec4 taylor_sin = ((-1.9515295891e-4f * x2 + Vec4::sReplicate(8.3321608736e-3f)) * x2 - Vec4::sReplicate(1.6666654611e-1f)) * x2 * x + x; // The lowest 2 bits of quadrant indicate the quadrant that we are in. // Let x be the original input value and x' our value that has been mapped to the range [-PI / 4, PI / 4]. // since cos(x) = sin(x - PI / 2) and since we want to use the Taylor expansion as close as possible to 0, // we can alternate between using the Taylor expansion for sin and cos according to the following table: // // quadrant sin(x) cos(x) // XXX00b sin(x') cos(x') // XXX01b cos(x') -sin(x') // XXX10b -sin(x') -cos(x') // XXX11b -cos(x') sin(x') // // So: sin_sign = bit2, cos_sign = bit1 ^ bit2, bit1 determines if we use sin or cos Taylor expansion UVec4 bit1 = quadrant.LogicalShiftLeft<31>(); UVec4 bit2 = UVec4::sAnd(quadrant.LogicalShiftLeft<30>(), UVec4::sReplicate(0x80000000U)); // Select which one of the results is sin and which one is cos Vec4 s = Vec4::sSelect(taylor_sin, taylor_cos, bit1); Vec4 c = Vec4::sSelect(taylor_cos, taylor_sin, bit1); // Update the signs sin_sign = UVec4::sXor(sin_sign, bit2); UVec4 cos_sign = UVec4::sXor(bit1, bit2); // Correct the signs outSin = Vec4::sXor(s, sin_sign.ReinterpretAsFloat()); outCos = Vec4::sXor(c, cos_sign.ReinterpretAsFloat()); } Vec4 Vec4::Tan() const { // Implementation based on tanf.c from the cephes library, see Vec4::SinCos for further details // Original implementation by Stephen L. Moshier (See: http://www.moshier.net/) // Make argument positive UVec4 tan_sign = UVec4::sAnd(ReinterpretAsInt(), UVec4::sReplicate(0x80000000U)); Vec4 x = Vec4::sXor(*this, tan_sign.ReinterpretAsFloat()); // 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