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GiantsTools/Sdk/External/DirectXMath/Inc/DirectXMathMisc.inl
Nick Blakely 71b675f5cb Update to new SDK.
2021-01-23 15:40:09 -08:00

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//-------------------------------------------------------------------------------------
// DirectXMathMisc.inl -- SIMD C++ Math library
//
// Copyright (c) Microsoft Corporation. All rights reserved.
// Licensed under the MIT License.
//
// http://go.microsoft.com/fwlink/?LinkID=615560
//-------------------------------------------------------------------------------------
#pragma once
/****************************************************************************
*
* Quaternion
*
****************************************************************************/
//------------------------------------------------------------------------------
// Comparison operations
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMQuaternionEqual
(
FXMVECTOR Q1,
FXMVECTOR Q2
) noexcept
{
return XMVector4Equal(Q1, Q2);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMQuaternionNotEqual
(
FXMVECTOR Q1,
FXMVECTOR Q2
) noexcept
{
return XMVector4NotEqual(Q1, Q2);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMQuaternionIsNaN(FXMVECTOR Q) noexcept
{
return XMVector4IsNaN(Q);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMQuaternionIsInfinite(FXMVECTOR Q) noexcept
{
return XMVector4IsInfinite(Q);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMQuaternionIsIdentity(FXMVECTOR Q) noexcept
{
return XMVector4Equal(Q, g_XMIdentityR3.v);
}
//------------------------------------------------------------------------------
// Computation operations
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionDot
(
FXMVECTOR Q1,
FXMVECTOR Q2
) noexcept
{
return XMVector4Dot(Q1, Q2);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionMultiply
(
FXMVECTOR Q1,
FXMVECTOR Q2
) noexcept
{
// Returns the product Q2*Q1 (which is the concatenation of a rotation Q1 followed by the rotation Q2)
// [ (Q2.w * Q1.x) + (Q2.x * Q1.w) + (Q2.y * Q1.z) - (Q2.z * Q1.y),
// (Q2.w * Q1.y) - (Q2.x * Q1.z) + (Q2.y * Q1.w) + (Q2.z * Q1.x),
// (Q2.w * Q1.z) + (Q2.x * Q1.y) - (Q2.y * Q1.x) + (Q2.z * Q1.w),
// (Q2.w * Q1.w) - (Q2.x * Q1.x) - (Q2.y * Q1.y) - (Q2.z * Q1.z) ]
#if defined(_XM_NO_INTRINSICS_)
XMVECTORF32 Result = { { {
(Q2.vector4_f32[3] * Q1.vector4_f32[0]) + (Q2.vector4_f32[0] * Q1.vector4_f32[3]) + (Q2.vector4_f32[1] * Q1.vector4_f32[2]) - (Q2.vector4_f32[2] * Q1.vector4_f32[1]),
(Q2.vector4_f32[3] * Q1.vector4_f32[1]) - (Q2.vector4_f32[0] * Q1.vector4_f32[2]) + (Q2.vector4_f32[1] * Q1.vector4_f32[3]) + (Q2.vector4_f32[2] * Q1.vector4_f32[0]),
(Q2.vector4_f32[3] * Q1.vector4_f32[2]) + (Q2.vector4_f32[0] * Q1.vector4_f32[1]) - (Q2.vector4_f32[1] * Q1.vector4_f32[0]) + (Q2.vector4_f32[2] * Q1.vector4_f32[3]),
(Q2.vector4_f32[3] * Q1.vector4_f32[3]) - (Q2.vector4_f32[0] * Q1.vector4_f32[0]) - (Q2.vector4_f32[1] * Q1.vector4_f32[1]) - (Q2.vector4_f32[2] * Q1.vector4_f32[2])
} } };
return Result.v;
#elif defined(_XM_ARM_NEON_INTRINSICS_)
static const XMVECTORF32 ControlWZYX = { { { 1.0f, -1.0f, 1.0f, -1.0f } } };
static const XMVECTORF32 ControlZWXY = { { { 1.0f, 1.0f, -1.0f, -1.0f } } };
static const XMVECTORF32 ControlYXWZ = { { { -1.0f, 1.0f, 1.0f, -1.0f } } };
float32x2_t Q2L = vget_low_f32(Q2);
float32x2_t Q2H = vget_high_f32(Q2);
float32x4_t Q2X = vdupq_lane_f32(Q2L, 0);
float32x4_t Q2Y = vdupq_lane_f32(Q2L, 1);
float32x4_t Q2Z = vdupq_lane_f32(Q2H, 0);
XMVECTOR vResult = vmulq_lane_f32(Q1, Q2H, 1);
// Mul by Q1WZYX
float32x4_t vTemp = vrev64q_f32(Q1);
vTemp = vcombine_f32(vget_high_f32(vTemp), vget_low_f32(vTemp));
Q2X = vmulq_f32(Q2X, vTemp);
vResult = vmlaq_f32(vResult, Q2X, ControlWZYX);
// Mul by Q1ZWXY
vTemp = vreinterpretq_f32_u32(vrev64q_u32(vreinterpretq_u32_f32(vTemp)));
Q2Y = vmulq_f32(Q2Y, vTemp);
vResult = vmlaq_f32(vResult, Q2Y, ControlZWXY);
// Mul by Q1YXWZ
vTemp = vreinterpretq_f32_u32(vrev64q_u32(vreinterpretq_u32_f32(vTemp)));
vTemp = vcombine_f32(vget_high_f32(vTemp), vget_low_f32(vTemp));
Q2Z = vmulq_f32(Q2Z, vTemp);
vResult = vmlaq_f32(vResult, Q2Z, ControlYXWZ);
return vResult;
#elif defined(_XM_SSE_INTRINSICS_)
static const XMVECTORF32 ControlWZYX = { { { 1.0f, -1.0f, 1.0f, -1.0f } } };
static const XMVECTORF32 ControlZWXY = { { { 1.0f, 1.0f, -1.0f, -1.0f } } };
static const XMVECTORF32 ControlYXWZ = { { { -1.0f, 1.0f, 1.0f, -1.0f } } };
// Copy to SSE registers and use as few as possible for x86
XMVECTOR Q2X = Q2;
XMVECTOR Q2Y = Q2;
XMVECTOR Q2Z = Q2;
XMVECTOR vResult = Q2;
// Splat with one instruction
vResult = XM_PERMUTE_PS(vResult, _MM_SHUFFLE(3, 3, 3, 3));
Q2X = XM_PERMUTE_PS(Q2X, _MM_SHUFFLE(0, 0, 0, 0));
Q2Y = XM_PERMUTE_PS(Q2Y, _MM_SHUFFLE(1, 1, 1, 1));
Q2Z = XM_PERMUTE_PS(Q2Z, _MM_SHUFFLE(2, 2, 2, 2));
// Retire Q1 and perform Q1*Q2W
vResult = _mm_mul_ps(vResult, Q1);
XMVECTOR Q1Shuffle = Q1;
// Shuffle the copies of Q1
Q1Shuffle = XM_PERMUTE_PS(Q1Shuffle, _MM_SHUFFLE(0, 1, 2, 3));
// Mul by Q1WZYX
Q2X = _mm_mul_ps(Q2X, Q1Shuffle);
Q1Shuffle = XM_PERMUTE_PS(Q1Shuffle, _MM_SHUFFLE(2, 3, 0, 1));
// Flip the signs on y and z
vResult = XM_FMADD_PS(Q2X, ControlWZYX, vResult);
// Mul by Q1ZWXY
Q2Y = _mm_mul_ps(Q2Y, Q1Shuffle);
Q1Shuffle = XM_PERMUTE_PS(Q1Shuffle, _MM_SHUFFLE(0, 1, 2, 3));
// Flip the signs on z and w
Q2Y = _mm_mul_ps(Q2Y, ControlZWXY);
// Mul by Q1YXWZ
Q2Z = _mm_mul_ps(Q2Z, Q1Shuffle);
// Flip the signs on x and w
Q2Y = XM_FMADD_PS(Q2Z, ControlYXWZ, Q2Y);
vResult = _mm_add_ps(vResult, Q2Y);
return vResult;
#endif
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionLengthSq(FXMVECTOR Q) noexcept
{
return XMVector4LengthSq(Q);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionReciprocalLength(FXMVECTOR Q) noexcept
{
return XMVector4ReciprocalLength(Q);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionLength(FXMVECTOR Q) noexcept
{
return XMVector4Length(Q);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionNormalizeEst(FXMVECTOR Q) noexcept
{
return XMVector4NormalizeEst(Q);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionNormalize(FXMVECTOR Q) noexcept
{
return XMVector4Normalize(Q);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionConjugate(FXMVECTOR Q) noexcept
{
#if defined(_XM_NO_INTRINSICS_)
XMVECTORF32 Result = { { {
-Q.vector4_f32[0],
-Q.vector4_f32[1],
-Q.vector4_f32[2],
Q.vector4_f32[3]
} } };
return Result.v;
#elif defined(_XM_ARM_NEON_INTRINSICS_)
static const XMVECTORF32 NegativeOne3 = { { { -1.0f, -1.0f, -1.0f, 1.0f } } };
return vmulq_f32(Q, NegativeOne3.v);
#elif defined(_XM_SSE_INTRINSICS_)
static const XMVECTORF32 NegativeOne3 = { { { -1.0f, -1.0f, -1.0f, 1.0f } } };
return _mm_mul_ps(Q, NegativeOne3);
#endif
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionInverse(FXMVECTOR Q) noexcept
{
const XMVECTOR Zero = XMVectorZero();
XMVECTOR L = XMVector4LengthSq(Q);
XMVECTOR Conjugate = XMQuaternionConjugate(Q);
XMVECTOR Control = XMVectorLessOrEqual(L, g_XMEpsilon.v);
XMVECTOR Result = XMVectorDivide(Conjugate, L);
Result = XMVectorSelect(Result, Zero, Control);
return Result;
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionLn(FXMVECTOR Q) noexcept
{
static const XMVECTORF32 OneMinusEpsilon = { { { 1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f } } };
XMVECTOR QW = XMVectorSplatW(Q);
XMVECTOR Q0 = XMVectorSelect(g_XMSelect1110.v, Q, g_XMSelect1110.v);
XMVECTOR ControlW = XMVectorInBounds(QW, OneMinusEpsilon.v);
XMVECTOR Theta = XMVectorACos(QW);
XMVECTOR SinTheta = XMVectorSin(Theta);
XMVECTOR S = XMVectorDivide(Theta, SinTheta);
XMVECTOR Result = XMVectorMultiply(Q0, S);
Result = XMVectorSelect(Q0, Result, ControlW);
return Result;
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionExp(FXMVECTOR Q) noexcept
{
XMVECTOR Theta = XMVector3Length(Q);
XMVECTOR SinTheta, CosTheta;
XMVectorSinCos(&SinTheta, &CosTheta, Theta);
XMVECTOR S = XMVectorDivide(SinTheta, Theta);
XMVECTOR Result = XMVectorMultiply(Q, S);
const XMVECTOR Zero = XMVectorZero();
XMVECTOR Control = XMVectorNearEqual(Theta, Zero, g_XMEpsilon.v);
Result = XMVectorSelect(Result, Q, Control);
Result = XMVectorSelect(CosTheta, Result, g_XMSelect1110.v);
return Result;
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionSlerp
(
FXMVECTOR Q0,
FXMVECTOR Q1,
float t
) noexcept
{
XMVECTOR T = XMVectorReplicate(t);
return XMQuaternionSlerpV(Q0, Q1, T);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionSlerpV
(
FXMVECTOR Q0,
FXMVECTOR Q1,
FXMVECTOR T
) noexcept
{
assert((XMVectorGetY(T) == XMVectorGetX(T)) && (XMVectorGetZ(T) == XMVectorGetX(T)) && (XMVectorGetW(T) == XMVectorGetX(T)));
// Result = Q0 * sin((1.0 - t) * Omega) / sin(Omega) + Q1 * sin(t * Omega) / sin(Omega)
#if defined(_XM_NO_INTRINSICS_) || defined(_XM_ARM_NEON_INTRINSICS_)
const XMVECTORF32 OneMinusEpsilon = { { { 1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f } } };
XMVECTOR CosOmega = XMQuaternionDot(Q0, Q1);
const XMVECTOR Zero = XMVectorZero();
XMVECTOR Control = XMVectorLess(CosOmega, Zero);
XMVECTOR Sign = XMVectorSelect(g_XMOne.v, g_XMNegativeOne.v, Control);
CosOmega = XMVectorMultiply(CosOmega, Sign);
Control = XMVectorLess(CosOmega, OneMinusEpsilon);
XMVECTOR SinOmega = XMVectorNegativeMultiplySubtract(CosOmega, CosOmega, g_XMOne.v);
SinOmega = XMVectorSqrt(SinOmega);
XMVECTOR Omega = XMVectorATan2(SinOmega, CosOmega);
XMVECTOR SignMask = XMVectorSplatSignMask();
XMVECTOR V01 = XMVectorShiftLeft(T, Zero, 2);
SignMask = XMVectorShiftLeft(SignMask, Zero, 3);
V01 = XMVectorXorInt(V01, SignMask);
V01 = XMVectorAdd(g_XMIdentityR0.v, V01);
XMVECTOR InvSinOmega = XMVectorReciprocal(SinOmega);
XMVECTOR S0 = XMVectorMultiply(V01, Omega);
S0 = XMVectorSin(S0);
S0 = XMVectorMultiply(S0, InvSinOmega);
S0 = XMVectorSelect(V01, S0, Control);
XMVECTOR S1 = XMVectorSplatY(S0);
S0 = XMVectorSplatX(S0);
S1 = XMVectorMultiply(S1, Sign);
XMVECTOR Result = XMVectorMultiply(Q0, S0);
Result = XMVectorMultiplyAdd(Q1, S1, Result);
return Result;
#elif defined(_XM_SSE_INTRINSICS_)
static const XMVECTORF32 OneMinusEpsilon = { { { 1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f } } };
static const XMVECTORU32 SignMask2 = { { { 0x80000000, 0x00000000, 0x00000000, 0x00000000 } } };
XMVECTOR CosOmega = XMQuaternionDot(Q0, Q1);
const XMVECTOR Zero = XMVectorZero();
XMVECTOR Control = XMVectorLess(CosOmega, Zero);
XMVECTOR Sign = XMVectorSelect(g_XMOne, g_XMNegativeOne, Control);
CosOmega = _mm_mul_ps(CosOmega, Sign);
Control = XMVectorLess(CosOmega, OneMinusEpsilon);
XMVECTOR SinOmega = _mm_mul_ps(CosOmega, CosOmega);
SinOmega = _mm_sub_ps(g_XMOne, SinOmega);
SinOmega = _mm_sqrt_ps(SinOmega);
XMVECTOR Omega = XMVectorATan2(SinOmega, CosOmega);
XMVECTOR V01 = XM_PERMUTE_PS(T, _MM_SHUFFLE(2, 3, 0, 1));
V01 = _mm_and_ps(V01, g_XMMaskXY);
V01 = _mm_xor_ps(V01, SignMask2);
V01 = _mm_add_ps(g_XMIdentityR0, V01);
XMVECTOR S0 = _mm_mul_ps(V01, Omega);
S0 = XMVectorSin(S0);
S0 = _mm_div_ps(S0, SinOmega);
S0 = XMVectorSelect(V01, S0, Control);
XMVECTOR S1 = XMVectorSplatY(S0);
S0 = XMVectorSplatX(S0);
S1 = _mm_mul_ps(S1, Sign);
XMVECTOR Result = _mm_mul_ps(Q0, S0);
S1 = _mm_mul_ps(S1, Q1);
Result = _mm_add_ps(Result, S1);
return Result;
#endif
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionSquad
(
FXMVECTOR Q0,
FXMVECTOR Q1,
FXMVECTOR Q2,
GXMVECTOR Q3,
float t
) noexcept
{
XMVECTOR T = XMVectorReplicate(t);
return XMQuaternionSquadV(Q0, Q1, Q2, Q3, T);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionSquadV
(
FXMVECTOR Q0,
FXMVECTOR Q1,
FXMVECTOR Q2,
GXMVECTOR Q3,
HXMVECTOR T
) noexcept
{
assert((XMVectorGetY(T) == XMVectorGetX(T)) && (XMVectorGetZ(T) == XMVectorGetX(T)) && (XMVectorGetW(T) == XMVectorGetX(T)));
XMVECTOR TP = T;
const XMVECTOR Two = XMVectorSplatConstant(2, 0);
XMVECTOR Q03 = XMQuaternionSlerpV(Q0, Q3, T);
XMVECTOR Q12 = XMQuaternionSlerpV(Q1, Q2, T);
TP = XMVectorNegativeMultiplySubtract(TP, TP, TP);
TP = XMVectorMultiply(TP, Two);
XMVECTOR Result = XMQuaternionSlerpV(Q03, Q12, TP);
return Result;
}
//------------------------------------------------------------------------------
_Use_decl_annotations_
inline void XM_CALLCONV XMQuaternionSquadSetup
(
XMVECTOR* pA,
XMVECTOR* pB,
XMVECTOR* pC,
FXMVECTOR Q0,
FXMVECTOR Q1,
FXMVECTOR Q2,
GXMVECTOR Q3
) noexcept
{
assert(pA);
assert(pB);
assert(pC);
XMVECTOR LS12 = XMQuaternionLengthSq(XMVectorAdd(Q1, Q2));
XMVECTOR LD12 = XMQuaternionLengthSq(XMVectorSubtract(Q1, Q2));
XMVECTOR SQ2 = XMVectorNegate(Q2);
XMVECTOR Control1 = XMVectorLess(LS12, LD12);
SQ2 = XMVectorSelect(Q2, SQ2, Control1);
XMVECTOR LS01 = XMQuaternionLengthSq(XMVectorAdd(Q0, Q1));
XMVECTOR LD01 = XMQuaternionLengthSq(XMVectorSubtract(Q0, Q1));
XMVECTOR SQ0 = XMVectorNegate(Q0);
XMVECTOR LS23 = XMQuaternionLengthSq(XMVectorAdd(SQ2, Q3));
XMVECTOR LD23 = XMQuaternionLengthSq(XMVectorSubtract(SQ2, Q3));
XMVECTOR SQ3 = XMVectorNegate(Q3);
XMVECTOR Control0 = XMVectorLess(LS01, LD01);
XMVECTOR Control2 = XMVectorLess(LS23, LD23);
SQ0 = XMVectorSelect(Q0, SQ0, Control0);
SQ3 = XMVectorSelect(Q3, SQ3, Control2);
XMVECTOR InvQ1 = XMQuaternionInverse(Q1);
XMVECTOR InvQ2 = XMQuaternionInverse(SQ2);
XMVECTOR LnQ0 = XMQuaternionLn(XMQuaternionMultiply(InvQ1, SQ0));
XMVECTOR LnQ2 = XMQuaternionLn(XMQuaternionMultiply(InvQ1, SQ2));
XMVECTOR LnQ1 = XMQuaternionLn(XMQuaternionMultiply(InvQ2, Q1));
XMVECTOR LnQ3 = XMQuaternionLn(XMQuaternionMultiply(InvQ2, SQ3));
const XMVECTOR NegativeOneQuarter = XMVectorSplatConstant(-1, 2);
XMVECTOR ExpQ02 = XMVectorMultiply(XMVectorAdd(LnQ0, LnQ2), NegativeOneQuarter);
XMVECTOR ExpQ13 = XMVectorMultiply(XMVectorAdd(LnQ1, LnQ3), NegativeOneQuarter);
ExpQ02 = XMQuaternionExp(ExpQ02);
ExpQ13 = XMQuaternionExp(ExpQ13);
*pA = XMQuaternionMultiply(Q1, ExpQ02);
*pB = XMQuaternionMultiply(SQ2, ExpQ13);
*pC = SQ2;
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionBaryCentric
(
FXMVECTOR Q0,
FXMVECTOR Q1,
FXMVECTOR Q2,
float f,
float g
) noexcept
{
float s = f + g;
XMVECTOR Result;
if ((s < 0.00001f) && (s > -0.00001f))
{
Result = Q0;
}
else
{
XMVECTOR Q01 = XMQuaternionSlerp(Q0, Q1, s);
XMVECTOR Q02 = XMQuaternionSlerp(Q0, Q2, s);
Result = XMQuaternionSlerp(Q01, Q02, g / s);
}
return Result;
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionBaryCentricV
(
FXMVECTOR Q0,
FXMVECTOR Q1,
FXMVECTOR Q2,
GXMVECTOR F,
HXMVECTOR G
) noexcept
{
assert((XMVectorGetY(F) == XMVectorGetX(F)) && (XMVectorGetZ(F) == XMVectorGetX(F)) && (XMVectorGetW(F) == XMVectorGetX(F)));
assert((XMVectorGetY(G) == XMVectorGetX(G)) && (XMVectorGetZ(G) == XMVectorGetX(G)) && (XMVectorGetW(G) == XMVectorGetX(G)));
const XMVECTOR Epsilon = XMVectorSplatConstant(1, 16);
XMVECTOR S = XMVectorAdd(F, G);
XMVECTOR Result;
if (XMVector4InBounds(S, Epsilon))
{
Result = Q0;
}
else
{
XMVECTOR Q01 = XMQuaternionSlerpV(Q0, Q1, S);
XMVECTOR Q02 = XMQuaternionSlerpV(Q0, Q2, S);
XMVECTOR GS = XMVectorReciprocal(S);
GS = XMVectorMultiply(G, GS);
Result = XMQuaternionSlerpV(Q01, Q02, GS);
}
return Result;
}
//------------------------------------------------------------------------------
// Transformation operations
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionIdentity() noexcept
{
return g_XMIdentityR3.v;
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionRotationRollPitchYaw
(
float Pitch,
float Yaw,
float Roll
) noexcept
{
XMVECTOR Angles = XMVectorSet(Pitch, Yaw, Roll, 0.0f);
XMVECTOR Q = XMQuaternionRotationRollPitchYawFromVector(Angles);
return Q;
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionRotationRollPitchYawFromVector
(
FXMVECTOR Angles // <Pitch, Yaw, Roll, 0>
) noexcept
{
static const XMVECTORF32 Sign = { { { 1.0f, -1.0f, -1.0f, 1.0f } } };
XMVECTOR HalfAngles = XMVectorMultiply(Angles, g_XMOneHalf.v);
XMVECTOR SinAngles, CosAngles;
XMVectorSinCos(&SinAngles, &CosAngles, HalfAngles);
XMVECTOR P0 = XMVectorPermute<XM_PERMUTE_0X, XM_PERMUTE_1X, XM_PERMUTE_1X, XM_PERMUTE_1X>(SinAngles, CosAngles);
XMVECTOR Y0 = XMVectorPermute<XM_PERMUTE_1Y, XM_PERMUTE_0Y, XM_PERMUTE_1Y, XM_PERMUTE_1Y>(SinAngles, CosAngles);
XMVECTOR R0 = XMVectorPermute<XM_PERMUTE_1Z, XM_PERMUTE_1Z, XM_PERMUTE_0Z, XM_PERMUTE_1Z>(SinAngles, CosAngles);
XMVECTOR P1 = XMVectorPermute<XM_PERMUTE_0X, XM_PERMUTE_1X, XM_PERMUTE_1X, XM_PERMUTE_1X>(CosAngles, SinAngles);
XMVECTOR Y1 = XMVectorPermute<XM_PERMUTE_1Y, XM_PERMUTE_0Y, XM_PERMUTE_1Y, XM_PERMUTE_1Y>(CosAngles, SinAngles);
XMVECTOR R1 = XMVectorPermute<XM_PERMUTE_1Z, XM_PERMUTE_1Z, XM_PERMUTE_0Z, XM_PERMUTE_1Z>(CosAngles, SinAngles);
XMVECTOR Q1 = XMVectorMultiply(P1, Sign.v);
XMVECTOR Q0 = XMVectorMultiply(P0, Y0);
Q1 = XMVectorMultiply(Q1, Y1);
Q0 = XMVectorMultiply(Q0, R0);
XMVECTOR Q = XMVectorMultiplyAdd(Q1, R1, Q0);
return Q;
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionRotationNormal
(
FXMVECTOR NormalAxis,
float Angle
) noexcept
{
#if defined(_XM_NO_INTRINSICS_) || defined(_XM_ARM_NEON_INTRINSICS_)
XMVECTOR N = XMVectorSelect(g_XMOne.v, NormalAxis, g_XMSelect1110.v);
float SinV, CosV;
XMScalarSinCos(&SinV, &CosV, 0.5f * Angle);
XMVECTOR Scale = XMVectorSet(SinV, SinV, SinV, CosV);
return XMVectorMultiply(N, Scale);
#elif defined(_XM_SSE_INTRINSICS_)
XMVECTOR N = _mm_and_ps(NormalAxis, g_XMMask3);
N = _mm_or_ps(N, g_XMIdentityR3);
XMVECTOR Scale = _mm_set_ps1(0.5f * Angle);
XMVECTOR vSine;
XMVECTOR vCosine;
XMVectorSinCos(&vSine, &vCosine, Scale);
Scale = _mm_and_ps(vSine, g_XMMask3);
vCosine = _mm_and_ps(vCosine, g_XMMaskW);
Scale = _mm_or_ps(Scale, vCosine);
N = _mm_mul_ps(N, Scale);
return N;
#endif
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionRotationAxis
(
FXMVECTOR Axis,
float Angle
) noexcept
{
assert(!XMVector3Equal(Axis, XMVectorZero()));
assert(!XMVector3IsInfinite(Axis));
XMVECTOR Normal = XMVector3Normalize(Axis);
XMVECTOR Q = XMQuaternionRotationNormal(Normal, Angle);
return Q;
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionRotationMatrix(FXMMATRIX M) noexcept
{
#if defined(_XM_NO_INTRINSICS_)
XMVECTORF32 q;
float r22 = M.m[2][2];
if (r22 <= 0.f) // x^2 + y^2 >= z^2 + w^2
{
float dif10 = M.m[1][1] - M.m[0][0];
float omr22 = 1.f - r22;
if (dif10 <= 0.f) // x^2 >= y^2
{
float fourXSqr = omr22 - dif10;
float inv4x = 0.5f / sqrtf(fourXSqr);
q.f[0] = fourXSqr * inv4x;
q.f[1] = (M.m[0][1] + M.m[1][0]) * inv4x;
q.f[2] = (M.m[0][2] + M.m[2][0]) * inv4x;
q.f[3] = (M.m[1][2] - M.m[2][1]) * inv4x;
}
else // y^2 >= x^2
{
float fourYSqr = omr22 + dif10;
float inv4y = 0.5f / sqrtf(fourYSqr);
q.f[0] = (M.m[0][1] + M.m[1][0]) * inv4y;
q.f[1] = fourYSqr * inv4y;
q.f[2] = (M.m[1][2] + M.m[2][1]) * inv4y;
q.f[3] = (M.m[2][0] - M.m[0][2]) * inv4y;
}
}
else // z^2 + w^2 >= x^2 + y^2
{
float sum10 = M.m[1][1] + M.m[0][0];
float opr22 = 1.f + r22;
if (sum10 <= 0.f) // z^2 >= w^2
{
float fourZSqr = opr22 - sum10;
float inv4z = 0.5f / sqrtf(fourZSqr);
q.f[0] = (M.m[0][2] + M.m[2][0]) * inv4z;
q.f[1] = (M.m[1][2] + M.m[2][1]) * inv4z;
q.f[2] = fourZSqr * inv4z;
q.f[3] = (M.m[0][1] - M.m[1][0]) * inv4z;
}
else // w^2 >= z^2
{
float fourWSqr = opr22 + sum10;
float inv4w = 0.5f / sqrtf(fourWSqr);
q.f[0] = (M.m[1][2] - M.m[2][1]) * inv4w;
q.f[1] = (M.m[2][0] - M.m[0][2]) * inv4w;
q.f[2] = (M.m[0][1] - M.m[1][0]) * inv4w;
q.f[3] = fourWSqr * inv4w;
}
}
return q.v;
#elif defined(_XM_ARM_NEON_INTRINSICS_)
static const XMVECTORF32 XMPMMP = { { { +1.0f, -1.0f, -1.0f, +1.0f } } };
static const XMVECTORF32 XMMPMP = { { { -1.0f, +1.0f, -1.0f, +1.0f } } };
static const XMVECTORF32 XMMMPP = { { { -1.0f, -1.0f, +1.0f, +1.0f } } };
static const XMVECTORU32 Select0110 = { { { XM_SELECT_0, XM_SELECT_1, XM_SELECT_1, XM_SELECT_0 } } };
static const XMVECTORU32 Select0010 = { { { XM_SELECT_0, XM_SELECT_0, XM_SELECT_1, XM_SELECT_0 } } };
float32x4_t r0 = M.r[0];
float32x4_t r1 = M.r[1];
float32x4_t r2 = M.r[2];
float32x4_t r00 = vdupq_lane_f32(vget_low_f32(r0), 0);
float32x4_t r11 = vdupq_lane_f32(vget_low_f32(r1), 1);
float32x4_t r22 = vdupq_lane_f32(vget_high_f32(r2), 0);
// x^2 >= y^2 equivalent to r11 - r00 <= 0
float32x4_t r11mr00 = vsubq_f32(r11, r00);
uint32x4_t x2gey2 = vcleq_f32(r11mr00, g_XMZero);
// z^2 >= w^2 equivalent to r11 + r00 <= 0
float32x4_t r11pr00 = vaddq_f32(r11, r00);
uint32x4_t z2gew2 = vcleq_f32(r11pr00, g_XMZero);
// x^2 + y^2 >= z^2 + w^2 equivalent to r22 <= 0
uint32x4_t x2py2gez2pw2 = vcleq_f32(r22, g_XMZero);
// (4*x^2, 4*y^2, 4*z^2, 4*w^2)
float32x4_t t0 = vmulq_f32(XMPMMP, r00);
float32x4_t x2y2z2w2 = vmlaq_f32(t0, XMMPMP, r11);
x2y2z2w2 = vmlaq_f32(x2y2z2w2, XMMMPP, r22);
x2y2z2w2 = vaddq_f32(x2y2z2w2, g_XMOne);
// (r01, r02, r12, r11)
t0 = vextq_f32(r0, r0, 1);
float32x4_t t1 = vextq_f32(r1, r1, 1);
t0 = vcombine_f32(vget_low_f32(t0), vrev64_f32(vget_low_f32(t1)));
// (r10, r20, r21, r10)
t1 = vextq_f32(r2, r2, 3);
float32x4_t r10 = vdupq_lane_f32(vget_low_f32(r1), 0);
t1 = vbslq_f32(Select0110, t1, r10);
// (4*x*y, 4*x*z, 4*y*z, unused)
float32x4_t xyxzyz = vaddq_f32(t0, t1);
// (r21, r20, r10, r10)
t0 = vcombine_f32(vrev64_f32(vget_low_f32(r2)), vget_low_f32(r10));
// (r12, r02, r01, r12)
float32x4_t t2 = vcombine_f32(vrev64_f32(vget_high_f32(r0)), vrev64_f32(vget_low_f32(r0)));
float32x4_t t3 = vdupq_lane_f32(vget_high_f32(r1), 0);
t1 = vbslq_f32(Select0110, t2, t3);
// (4*x*w, 4*y*w, 4*z*w, unused)
float32x4_t xwywzw = vsubq_f32(t0, t1);
xwywzw = vmulq_f32(XMMPMP, xwywzw);
// (4*x*x, 4*x*y, 4*x*z, 4*x*w)
t0 = vextq_f32(xyxzyz, xyxzyz, 3);
t1 = vbslq_f32(Select0110, t0, x2y2z2w2);
t2 = vdupq_lane_f32(vget_low_f32(xwywzw), 0);
float32x4_t tensor0 = vbslq_f32(g_XMSelect1110, t1, t2);
// (4*y*x, 4*y*y, 4*y*z, 4*y*w)
t0 = vbslq_f32(g_XMSelect1011, xyxzyz, x2y2z2w2);
t1 = vdupq_lane_f32(vget_low_f32(xwywzw), 1);
float32x4_t tensor1 = vbslq_f32(g_XMSelect1110, t0, t1);
// (4*z*x, 4*z*y, 4*z*z, 4*z*w)
t0 = vextq_f32(xyxzyz, xyxzyz, 1);
t1 = vcombine_f32(vget_low_f32(t0), vrev64_f32(vget_high_f32(xwywzw)));
float32x4_t tensor2 = vbslq_f32(Select0010, x2y2z2w2, t1);
// (4*w*x, 4*w*y, 4*w*z, 4*w*w)
float32x4_t tensor3 = vbslq_f32(g_XMSelect1110, xwywzw, x2y2z2w2);
// Select the row of the tensor-product matrix that has the largest
// magnitude.
t0 = vbslq_f32(x2gey2, tensor0, tensor1);
t1 = vbslq_f32(z2gew2, tensor2, tensor3);
t2 = vbslq_f32(x2py2gez2pw2, t0, t1);
// Normalize the row. No division by zero is possible because the
// quaternion is unit-length (and the row is a nonzero multiple of
// the quaternion).
t0 = XMVector4Length(t2);
return XMVectorDivide(t2, t0);
#elif defined(_XM_SSE_INTRINSICS_)
static const XMVECTORF32 XMPMMP = { { { +1.0f, -1.0f, -1.0f, +1.0f } } };
static const XMVECTORF32 XMMPMP = { { { -1.0f, +1.0f, -1.0f, +1.0f } } };
static const XMVECTORF32 XMMMPP = { { { -1.0f, -1.0f, +1.0f, +1.0f } } };
XMVECTOR r0 = M.r[0]; // (r00, r01, r02, 0)
XMVECTOR r1 = M.r[1]; // (r10, r11, r12, 0)
XMVECTOR r2 = M.r[2]; // (r20, r21, r22, 0)
// (r00, r00, r00, r00)
XMVECTOR r00 = XM_PERMUTE_PS(r0, _MM_SHUFFLE(0, 0, 0, 0));
// (r11, r11, r11, r11)
XMVECTOR r11 = XM_PERMUTE_PS(r1, _MM_SHUFFLE(1, 1, 1, 1));
// (r22, r22, r22, r22)
XMVECTOR r22 = XM_PERMUTE_PS(r2, _MM_SHUFFLE(2, 2, 2, 2));
// x^2 >= y^2 equivalent to r11 - r00 <= 0
// (r11 - r00, r11 - r00, r11 - r00, r11 - r00)
XMVECTOR r11mr00 = _mm_sub_ps(r11, r00);
XMVECTOR x2gey2 = _mm_cmple_ps(r11mr00, g_XMZero);
// z^2 >= w^2 equivalent to r11 + r00 <= 0
// (r11 + r00, r11 + r00, r11 + r00, r11 + r00)
XMVECTOR r11pr00 = _mm_add_ps(r11, r00);
XMVECTOR z2gew2 = _mm_cmple_ps(r11pr00, g_XMZero);
// x^2 + y^2 >= z^2 + w^2 equivalent to r22 <= 0
XMVECTOR x2py2gez2pw2 = _mm_cmple_ps(r22, g_XMZero);
// (4*x^2, 4*y^2, 4*z^2, 4*w^2)
XMVECTOR t0 = XM_FMADD_PS(XMPMMP, r00, g_XMOne);
XMVECTOR t1 = _mm_mul_ps(XMMPMP, r11);
XMVECTOR t2 = XM_FMADD_PS(XMMMPP, r22, t0);
XMVECTOR x2y2z2w2 = _mm_add_ps(t1, t2);
// (r01, r02, r12, r11)
t0 = _mm_shuffle_ps(r0, r1, _MM_SHUFFLE(1, 2, 2, 1));
// (r10, r10, r20, r21)
t1 = _mm_shuffle_ps(r1, r2, _MM_SHUFFLE(1, 0, 0, 0));
// (r10, r20, r21, r10)
t1 = XM_PERMUTE_PS(t1, _MM_SHUFFLE(1, 3, 2, 0));
// (4*x*y, 4*x*z, 4*y*z, unused)
XMVECTOR xyxzyz = _mm_add_ps(t0, t1);
// (r21, r20, r10, r10)
t0 = _mm_shuffle_ps(r2, r1, _MM_SHUFFLE(0, 0, 0, 1));
// (r12, r12, r02, r01)
t1 = _mm_shuffle_ps(r1, r0, _MM_SHUFFLE(1, 2, 2, 2));
// (r12, r02, r01, r12)
t1 = XM_PERMUTE_PS(t1, _MM_SHUFFLE(1, 3, 2, 0));
// (4*x*w, 4*y*w, 4*z*w, unused)
XMVECTOR xwywzw = _mm_sub_ps(t0, t1);
xwywzw = _mm_mul_ps(XMMPMP, xwywzw);
// (4*x^2, 4*y^2, 4*x*y, unused)
t0 = _mm_shuffle_ps(x2y2z2w2, xyxzyz, _MM_SHUFFLE(0, 0, 1, 0));
// (4*z^2, 4*w^2, 4*z*w, unused)
t1 = _mm_shuffle_ps(x2y2z2w2, xwywzw, _MM_SHUFFLE(0, 2, 3, 2));
// (4*x*z, 4*y*z, 4*x*w, 4*y*w)
t2 = _mm_shuffle_ps(xyxzyz, xwywzw, _MM_SHUFFLE(1, 0, 2, 1));
// (4*x*x, 4*x*y, 4*x*z, 4*x*w)
XMVECTOR tensor0 = _mm_shuffle_ps(t0, t2, _MM_SHUFFLE(2, 0, 2, 0));
// (4*y*x, 4*y*y, 4*y*z, 4*y*w)
XMVECTOR tensor1 = _mm_shuffle_ps(t0, t2, _MM_SHUFFLE(3, 1, 1, 2));
// (4*z*x, 4*z*y, 4*z*z, 4*z*w)
XMVECTOR tensor2 = _mm_shuffle_ps(t2, t1, _MM_SHUFFLE(2, 0, 1, 0));
// (4*w*x, 4*w*y, 4*w*z, 4*w*w)
XMVECTOR tensor3 = _mm_shuffle_ps(t2, t1, _MM_SHUFFLE(1, 2, 3, 2));
// Select the row of the tensor-product matrix that has the largest
// magnitude.
t0 = _mm_and_ps(x2gey2, tensor0);
t1 = _mm_andnot_ps(x2gey2, tensor1);
t0 = _mm_or_ps(t0, t1);
t1 = _mm_and_ps(z2gew2, tensor2);
t2 = _mm_andnot_ps(z2gew2, tensor3);
t1 = _mm_or_ps(t1, t2);
t0 = _mm_and_ps(x2py2gez2pw2, t0);
t1 = _mm_andnot_ps(x2py2gez2pw2, t1);
t2 = _mm_or_ps(t0, t1);
// Normalize the row. No division by zero is possible because the
// quaternion is unit-length (and the row is a nonzero multiple of
// the quaternion).
t0 = XMVector4Length(t2);
return _mm_div_ps(t2, t0);
#endif
}
//------------------------------------------------------------------------------
// Conversion operations
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
_Use_decl_annotations_
inline void XM_CALLCONV XMQuaternionToAxisAngle
(
XMVECTOR* pAxis,
float* pAngle,
FXMVECTOR Q
) noexcept
{
assert(pAxis);
assert(pAngle);
*pAxis = Q;
*pAngle = 2.0f * XMScalarACos(XMVectorGetW(Q));
}
/****************************************************************************
*
* Plane
*
****************************************************************************/
//------------------------------------------------------------------------------
// Comparison operations
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMPlaneEqual
(
FXMVECTOR P1,
FXMVECTOR P2
) noexcept
{
return XMVector4Equal(P1, P2);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMPlaneNearEqual
(
FXMVECTOR P1,
FXMVECTOR P2,
FXMVECTOR Epsilon
) noexcept
{
XMVECTOR NP1 = XMPlaneNormalize(P1);
XMVECTOR NP2 = XMPlaneNormalize(P2);
return XMVector4NearEqual(NP1, NP2, Epsilon);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMPlaneNotEqual
(
FXMVECTOR P1,
FXMVECTOR P2
) noexcept
{
return XMVector4NotEqual(P1, P2);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMPlaneIsNaN(FXMVECTOR P) noexcept
{
return XMVector4IsNaN(P);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMPlaneIsInfinite(FXMVECTOR P) noexcept
{
return XMVector4IsInfinite(P);
}
//------------------------------------------------------------------------------
// Computation operations
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMPlaneDot
(
FXMVECTOR P,
FXMVECTOR V
) noexcept
{
return XMVector4Dot(P, V);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMPlaneDotCoord
(
FXMVECTOR P,
FXMVECTOR V
) noexcept
{
// Result = P[0] * V[0] + P[1] * V[1] + P[2] * V[2] + P[3]
XMVECTOR V3 = XMVectorSelect(g_XMOne.v, V, g_XMSelect1110.v);
XMVECTOR Result = XMVector4Dot(P, V3);
return Result;
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMPlaneDotNormal
(
FXMVECTOR P,
FXMVECTOR V
) noexcept
{
return XMVector3Dot(P, V);
}
//------------------------------------------------------------------------------
// XMPlaneNormalizeEst uses a reciprocal estimate and
// returns QNaN on zero and infinite vectors.
inline XMVECTOR XM_CALLCONV XMPlaneNormalizeEst(FXMVECTOR P) noexcept
{
#if defined(_XM_NO_INTRINSICS_) || defined(_XM_ARM_NEON_INTRINSICS_)
XMVECTOR Result = XMVector3ReciprocalLengthEst(P);
return XMVectorMultiply(P, Result);
#elif defined(_XM_SSE4_INTRINSICS_)
XMVECTOR vTemp = _mm_dp_ps(P, P, 0x7f);
XMVECTOR vResult = _mm_rsqrt_ps(vTemp);
return _mm_mul_ps(vResult, P);
#elif defined(_XM_SSE_INTRINSICS_)
// Perform the dot product
XMVECTOR vDot = _mm_mul_ps(P, P);
// x=Dot.y, y=Dot.z
XMVECTOR vTemp = XM_PERMUTE_PS(vDot, _MM_SHUFFLE(2, 1, 2, 1));
// Result.x = x+y
vDot = _mm_add_ss(vDot, vTemp);
// x=Dot.z
vTemp = XM_PERMUTE_PS(vTemp, _MM_SHUFFLE(1, 1, 1, 1));
// Result.x = (x+y)+z
vDot = _mm_add_ss(vDot, vTemp);
// Splat x
vDot = XM_PERMUTE_PS(vDot, _MM_SHUFFLE(0, 0, 0, 0));
// Get the reciprocal
vDot = _mm_rsqrt_ps(vDot);
// Get the reciprocal
vDot = _mm_mul_ps(vDot, P);
return vDot;
#endif
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMPlaneNormalize(FXMVECTOR P) noexcept
{
#if defined(_XM_NO_INTRINSICS_)
float fLengthSq = sqrtf((P.vector4_f32[0] * P.vector4_f32[0]) + (P.vector4_f32[1] * P.vector4_f32[1]) + (P.vector4_f32[2] * P.vector4_f32[2]));
// Prevent divide by zero
if (fLengthSq > 0)
{
fLengthSq = 1.0f / fLengthSq;
}
XMVECTORF32 vResult = { { {
P.vector4_f32[0] * fLengthSq,
P.vector4_f32[1] * fLengthSq,
P.vector4_f32[2] * fLengthSq,
P.vector4_f32[3] * fLengthSq
} } };
return vResult.v;
#elif defined(_XM_ARM_NEON_INTRINSICS_)
XMVECTOR vLength = XMVector3ReciprocalLength(P);
return XMVectorMultiply(P, vLength);
#elif defined(_XM_SSE4_INTRINSICS_)
XMVECTOR vLengthSq = _mm_dp_ps(P, P, 0x7f);
// Prepare for the division
XMVECTOR vResult = _mm_sqrt_ps(vLengthSq);
// Failsafe on zero (Or epsilon) length planes
// If the length is infinity, set the elements to zero
vLengthSq = _mm_cmpneq_ps(vLengthSq, g_XMInfinity);
// Reciprocal mul to perform the normalization
vResult = _mm_div_ps(P, vResult);
// Any that are infinity, set to zero
vResult = _mm_and_ps(vResult, vLengthSq);
return vResult;
#elif defined(_XM_SSE_INTRINSICS_)
// Perform the dot product on x,y and z only
XMVECTOR vLengthSq = _mm_mul_ps(P, P);
XMVECTOR vTemp = XM_PERMUTE_PS(vLengthSq, _MM_SHUFFLE(2, 1, 2, 1));
vLengthSq = _mm_add_ss(vLengthSq, vTemp);
vTemp = XM_PERMUTE_PS(vTemp, _MM_SHUFFLE(1, 1, 1, 1));
vLengthSq = _mm_add_ss(vLengthSq, vTemp);
vLengthSq = XM_PERMUTE_PS(vLengthSq, _MM_SHUFFLE(0, 0, 0, 0));
// Prepare for the division
XMVECTOR vResult = _mm_sqrt_ps(vLengthSq);
// Failsafe on zero (Or epsilon) length planes
// If the length is infinity, set the elements to zero
vLengthSq = _mm_cmpneq_ps(vLengthSq, g_XMInfinity);
// Reciprocal mul to perform the normalization
vResult = _mm_div_ps(P, vResult);
// Any that are infinity, set to zero
vResult = _mm_and_ps(vResult, vLengthSq);
return vResult;
#endif
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMPlaneIntersectLine
(
FXMVECTOR P,
FXMVECTOR LinePoint1,
FXMVECTOR LinePoint2
) noexcept
{
XMVECTOR V1 = XMVector3Dot(P, LinePoint1);
XMVECTOR V2 = XMVector3Dot(P, LinePoint2);
XMVECTOR D = XMVectorSubtract(V1, V2);
XMVECTOR VT = XMPlaneDotCoord(P, LinePoint1);
VT = XMVectorDivide(VT, D);
XMVECTOR Point = XMVectorSubtract(LinePoint2, LinePoint1);
Point = XMVectorMultiplyAdd(Point, VT, LinePoint1);
const XMVECTOR Zero = XMVectorZero();
XMVECTOR Control = XMVectorNearEqual(D, Zero, g_XMEpsilon.v);
return XMVectorSelect(Point, g_XMQNaN.v, Control);
}
//------------------------------------------------------------------------------
_Use_decl_annotations_
inline void XM_CALLCONV XMPlaneIntersectPlane
(
XMVECTOR* pLinePoint1,
XMVECTOR* pLinePoint2,
FXMVECTOR P1,
FXMVECTOR P2
) noexcept
{
assert(pLinePoint1);
assert(pLinePoint2);
XMVECTOR V1 = XMVector3Cross(P2, P1);
XMVECTOR LengthSq = XMVector3LengthSq(V1);
XMVECTOR V2 = XMVector3Cross(P2, V1);
XMVECTOR P1W = XMVectorSplatW(P1);
XMVECTOR Point = XMVectorMultiply(V2, P1W);
XMVECTOR V3 = XMVector3Cross(V1, P1);
XMVECTOR P2W = XMVectorSplatW(P2);
Point = XMVectorMultiplyAdd(V3, P2W, Point);
XMVECTOR LinePoint1 = XMVectorDivide(Point, LengthSq);
XMVECTOR LinePoint2 = XMVectorAdd(LinePoint1, V1);
XMVECTOR Control = XMVectorLessOrEqual(LengthSq, g_XMEpsilon.v);
*pLinePoint1 = XMVectorSelect(LinePoint1, g_XMQNaN.v, Control);
*pLinePoint2 = XMVectorSelect(LinePoint2, g_XMQNaN.v, Control);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMPlaneTransform
(
FXMVECTOR P,
FXMMATRIX M
) noexcept
{
XMVECTOR W = XMVectorSplatW(P);
XMVECTOR Z = XMVectorSplatZ(P);
XMVECTOR Y = XMVectorSplatY(P);
XMVECTOR X = XMVectorSplatX(P);
XMVECTOR Result = XMVectorMultiply(W, M.r[3]);
Result = XMVectorMultiplyAdd(Z, M.r[2], Result);
Result = XMVectorMultiplyAdd(Y, M.r[1], Result);
Result = XMVectorMultiplyAdd(X, M.r[0], Result);
return Result;
}
//------------------------------------------------------------------------------
_Use_decl_annotations_
inline XMFLOAT4* XM_CALLCONV XMPlaneTransformStream
(
XMFLOAT4* pOutputStream,
size_t OutputStride,
const XMFLOAT4* pInputStream,
size_t InputStride,
size_t PlaneCount,
FXMMATRIX M
) noexcept
{
return XMVector4TransformStream(pOutputStream,
OutputStride,
pInputStream,
InputStride,
PlaneCount,
M);
}
//------------------------------------------------------------------------------
// Conversion operations
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMPlaneFromPointNormal
(
FXMVECTOR Point,
FXMVECTOR Normal
) noexcept
{
XMVECTOR W = XMVector3Dot(Point, Normal);
W = XMVectorNegate(W);
return XMVectorSelect(W, Normal, g_XMSelect1110.v);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMPlaneFromPoints
(
FXMVECTOR Point1,
FXMVECTOR Point2,
FXMVECTOR Point3
) noexcept
{
XMVECTOR V21 = XMVectorSubtract(Point1, Point2);
XMVECTOR V31 = XMVectorSubtract(Point1, Point3);
XMVECTOR N = XMVector3Cross(V21, V31);
N = XMVector3Normalize(N);
XMVECTOR D = XMPlaneDotNormal(N, Point1);
D = XMVectorNegate(D);
XMVECTOR Result = XMVectorSelect(D, N, g_XMSelect1110.v);
return Result;
}
/****************************************************************************
*
* Color
*
****************************************************************************/
//------------------------------------------------------------------------------
// Comparison operations
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMColorEqual
(
FXMVECTOR C1,
FXMVECTOR C2
) noexcept
{
return XMVector4Equal(C1, C2);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMColorNotEqual
(
FXMVECTOR C1,
FXMVECTOR C2
) noexcept
{
return XMVector4NotEqual(C1, C2);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMColorGreater
(
FXMVECTOR C1,
FXMVECTOR C2
) noexcept
{
return XMVector4Greater(C1, C2);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMColorGreaterOrEqual
(
FXMVECTOR C1,
FXMVECTOR C2
) noexcept
{
return XMVector4GreaterOrEqual(C1, C2);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMColorLess
(
FXMVECTOR C1,
FXMVECTOR C2
) noexcept
{
return XMVector4Less(C1, C2);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMColorLessOrEqual
(
FXMVECTOR C1,
FXMVECTOR C2
) noexcept
{
return XMVector4LessOrEqual(C1, C2);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMColorIsNaN(FXMVECTOR C) noexcept
{
return XMVector4IsNaN(C);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMColorIsInfinite(FXMVECTOR C) noexcept
{
return XMVector4IsInfinite(C);
}
//------------------------------------------------------------------------------
// Computation operations
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMColorNegative(FXMVECTOR vColor) noexcept
{
#if defined(_XM_NO_INTRINSICS_)
XMVECTORF32 vResult = { { {
1.0f - vColor.vector4_f32[0],
1.0f - vColor.vector4_f32[1],
1.0f - vColor.vector4_f32[2],
vColor.vector4_f32[3]
} } };
return vResult.v;
#elif defined(_XM_ARM_NEON_INTRINSICS_)
uint32x4_t vTemp = veorq_u32(vreinterpretq_u32_f32(vColor), g_XMNegate3);
return vaddq_f32(vreinterpretq_f32_u32(vTemp), g_XMOne3);
#elif defined(_XM_SSE_INTRINSICS_)
// Negate only x,y and z.
XMVECTOR vTemp = _mm_xor_ps(vColor, g_XMNegate3);
// Add 1,1,1,0 to -x,-y,-z,w
return _mm_add_ps(vTemp, g_XMOne3);
#endif
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMColorModulate
(
FXMVECTOR C1,
FXMVECTOR C2
) noexcept
{
return XMVectorMultiply(C1, C2);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMColorAdjustSaturation
(
FXMVECTOR vColor,
float fSaturation
) noexcept
{
// Luminance = 0.2125f * C[0] + 0.7154f * C[1] + 0.0721f * C[2];
// Result = (C - Luminance) * Saturation + Luminance;
const XMVECTORF32 gvLuminance = { { { 0.2125f, 0.7154f, 0.0721f, 0.0f } } };
#if defined(_XM_NO_INTRINSICS_)
float fLuminance = (vColor.vector4_f32[0] * gvLuminance.f[0]) + (vColor.vector4_f32[1] * gvLuminance.f[1]) + (vColor.vector4_f32[2] * gvLuminance.f[2]);
XMVECTOR vResult;
vResult.vector4_f32[0] = ((vColor.vector4_f32[0] - fLuminance) * fSaturation) + fLuminance;
vResult.vector4_f32[1] = ((vColor.vector4_f32[1] - fLuminance) * fSaturation) + fLuminance;
vResult.vector4_f32[2] = ((vColor.vector4_f32[2] - fLuminance) * fSaturation) + fLuminance;
vResult.vector4_f32[3] = vColor.vector4_f32[3];
return vResult;
#elif defined(_XM_ARM_NEON_INTRINSICS_)
XMVECTOR vLuminance = XMVector3Dot(vColor, gvLuminance);
XMVECTOR vResult = vsubq_f32(vColor, vLuminance);
vResult = vmlaq_n_f32(vLuminance, vResult, fSaturation);
return vbslq_f32(g_XMSelect1110, vResult, vColor);
#elif defined(_XM_SSE_INTRINSICS_)
XMVECTOR vLuminance = XMVector3Dot(vColor, gvLuminance);
// Splat fSaturation
XMVECTOR vSaturation = _mm_set_ps1(fSaturation);
// vResult = ((vColor-vLuminance)*vSaturation)+vLuminance;
XMVECTOR vResult = _mm_sub_ps(vColor, vLuminance);
vResult = XM_FMADD_PS(vResult, vSaturation, vLuminance);
// Retain w from the source color
vLuminance = _mm_shuffle_ps(vResult, vColor, _MM_SHUFFLE(3, 2, 2, 2)); // x = vResult.z,y = vResult.z,z = vColor.z,w=vColor.w
vResult = _mm_shuffle_ps(vResult, vLuminance, _MM_SHUFFLE(3, 0, 1, 0)); // x = vResult.x,y = vResult.y,z = vResult.z,w=vColor.w
return vResult;
#endif
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMColorAdjustContrast
(
FXMVECTOR vColor,
float fContrast
) noexcept
{
// Result = (vColor - 0.5f) * fContrast + 0.5f;
#if defined(_XM_NO_INTRINSICS_)
XMVECTORF32 vResult = { { {
((vColor.vector4_f32[0] - 0.5f) * fContrast) + 0.5f,
((vColor.vector4_f32[1] - 0.5f) * fContrast) + 0.5f,
((vColor.vector4_f32[2] - 0.5f) * fContrast) + 0.5f,
vColor.vector4_f32[3] // Leave W untouched
} } };
return vResult.v;
#elif defined(_XM_ARM_NEON_INTRINSICS_)
XMVECTOR vResult = vsubq_f32(vColor, g_XMOneHalf.v);
vResult = vmlaq_n_f32(g_XMOneHalf.v, vResult, fContrast);
return vbslq_f32(g_XMSelect1110, vResult, vColor);
#elif defined(_XM_SSE_INTRINSICS_)
XMVECTOR vScale = _mm_set_ps1(fContrast); // Splat the scale
XMVECTOR vResult = _mm_sub_ps(vColor, g_XMOneHalf); // Subtract 0.5f from the source (Saving source)
vResult = XM_FMADD_PS(vResult, vScale, g_XMOneHalf);
// Retain w from the source color
vScale = _mm_shuffle_ps(vResult, vColor, _MM_SHUFFLE(3, 2, 2, 2)); // x = vResult.z,y = vResult.z,z = vColor.z,w=vColor.w
vResult = _mm_shuffle_ps(vResult, vScale, _MM_SHUFFLE(3, 0, 1, 0)); // x = vResult.x,y = vResult.y,z = vResult.z,w=vColor.w
return vResult;
#endif
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMColorRGBToHSL(FXMVECTOR rgb) noexcept
{
XMVECTOR r = XMVectorSplatX(rgb);
XMVECTOR g = XMVectorSplatY(rgb);
XMVECTOR b = XMVectorSplatZ(rgb);
XMVECTOR min = XMVectorMin(r, XMVectorMin(g, b));
XMVECTOR max = XMVectorMax(r, XMVectorMax(g, b));
XMVECTOR l = XMVectorMultiply(XMVectorAdd(min, max), g_XMOneHalf);
XMVECTOR d = XMVectorSubtract(max, min);
XMVECTOR la = XMVectorSelect(rgb, l, g_XMSelect1110);
if (XMVector3Less(d, g_XMEpsilon))
{
// Achromatic, assume H and S of 0
return XMVectorSelect(la, g_XMZero, g_XMSelect1100);
}
else
{
XMVECTOR s, h;
XMVECTOR d2 = XMVectorAdd(min, max);
if (XMVector3Greater(l, g_XMOneHalf))
{
// d / (2-max-min)
s = XMVectorDivide(d, XMVectorSubtract(g_XMTwo, d2));
}
else
{
// d / (max+min)
s = XMVectorDivide(d, d2);
}
if (XMVector3Equal(r, max))
{
// Red is max
h = XMVectorDivide(XMVectorSubtract(g, b), d);
}
else if (XMVector3Equal(g, max))
{
// Green is max
h = XMVectorDivide(XMVectorSubtract(b, r), d);
h = XMVectorAdd(h, g_XMTwo);
}
else
{
// Blue is max
h = XMVectorDivide(XMVectorSubtract(r, g), d);
h = XMVectorAdd(h, g_XMFour);
}
h = XMVectorDivide(h, g_XMSix);
if (XMVector3Less(h, g_XMZero))
h = XMVectorAdd(h, g_XMOne);
XMVECTOR lha = XMVectorSelect(la, h, g_XMSelect1100);
return XMVectorSelect(s, lha, g_XMSelect1011);
}
}
//------------------------------------------------------------------------------
namespace Internal
{
inline XMVECTOR XM_CALLCONV XMColorHue2Clr(FXMVECTOR p, FXMVECTOR q, FXMVECTOR h) noexcept
{
static const XMVECTORF32 oneSixth = { { { 1.0f / 6.0f, 1.0f / 6.0f, 1.0f / 6.0f, 1.0f / 6.0f } } };
static const XMVECTORF32 twoThirds = { { { 2.0f / 3.0f, 2.0f / 3.0f, 2.0f / 3.0f, 2.0f / 3.0f } } };
XMVECTOR t = h;
if (XMVector3Less(t, g_XMZero))
t = XMVectorAdd(t, g_XMOne);
if (XMVector3Greater(t, g_XMOne))
t = XMVectorSubtract(t, g_XMOne);
if (XMVector3Less(t, oneSixth))
{
// p + (q - p) * 6 * t
XMVECTOR t1 = XMVectorSubtract(q, p);
XMVECTOR t2 = XMVectorMultiply(g_XMSix, t);
return XMVectorMultiplyAdd(t1, t2, p);
}
if (XMVector3Less(t, g_XMOneHalf))
return q;
if (XMVector3Less(t, twoThirds))
{
// p + (q - p) * 6 * (2/3 - t)
XMVECTOR t1 = XMVectorSubtract(q, p);
XMVECTOR t2 = XMVectorMultiply(g_XMSix, XMVectorSubtract(twoThirds, t));
return XMVectorMultiplyAdd(t1, t2, p);
}
return p;
}
} // namespace Internal
inline XMVECTOR XM_CALLCONV XMColorHSLToRGB(FXMVECTOR hsl) noexcept
{
static const XMVECTORF32 oneThird = { { { 1.0f / 3.0f, 1.0f / 3.0f, 1.0f / 3.0f, 1.0f / 3.0f } } };
XMVECTOR s = XMVectorSplatY(hsl);
XMVECTOR l = XMVectorSplatZ(hsl);
if (XMVector3NearEqual(s, g_XMZero, g_XMEpsilon))
{
// Achromatic
return XMVectorSelect(hsl, l, g_XMSelect1110);
}
else
{
XMVECTOR h = XMVectorSplatX(hsl);
XMVECTOR q;
if (XMVector3Less(l, g_XMOneHalf))
{
q = XMVectorMultiply(l, XMVectorAdd(g_XMOne, s));
}
else
{
q = XMVectorSubtract(XMVectorAdd(l, s), XMVectorMultiply(l, s));
}
XMVECTOR p = XMVectorSubtract(XMVectorMultiply(g_XMTwo, l), q);
XMVECTOR r = DirectX::Internal::XMColorHue2Clr(p, q, XMVectorAdd(h, oneThird));
XMVECTOR g = DirectX::Internal::XMColorHue2Clr(p, q, h);
XMVECTOR b = DirectX::Internal::XMColorHue2Clr(p, q, XMVectorSubtract(h, oneThird));
XMVECTOR rg = XMVectorSelect(g, r, g_XMSelect1000);
XMVECTOR ba = XMVectorSelect(hsl, b, g_XMSelect1110);
return XMVectorSelect(ba, rg, g_XMSelect1100);
}
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMColorRGBToHSV(FXMVECTOR rgb) noexcept
{
XMVECTOR r = XMVectorSplatX(rgb);
XMVECTOR g = XMVectorSplatY(rgb);
XMVECTOR b = XMVectorSplatZ(rgb);
XMVECTOR min = XMVectorMin(r, XMVectorMin(g, b));
XMVECTOR v = XMVectorMax(r, XMVectorMax(g, b));
XMVECTOR d = XMVectorSubtract(v, min);
XMVECTOR s = (XMVector3NearEqual(v, g_XMZero, g_XMEpsilon)) ? g_XMZero : XMVectorDivide(d, v);
if (XMVector3Less(d, g_XMEpsilon))
{
// Achromatic, assume H of 0
XMVECTOR hv = XMVectorSelect(v, g_XMZero, g_XMSelect1000);
XMVECTOR hva = XMVectorSelect(rgb, hv, g_XMSelect1110);
return XMVectorSelect(s, hva, g_XMSelect1011);
}
else
{
XMVECTOR h;
if (XMVector3Equal(r, v))
{
// Red is max
h = XMVectorDivide(XMVectorSubtract(g, b), d);
if (XMVector3Less(g, b))
h = XMVectorAdd(h, g_XMSix);
}
else if (XMVector3Equal(g, v))
{
// Green is max
h = XMVectorDivide(XMVectorSubtract(b, r), d);
h = XMVectorAdd(h, g_XMTwo);
}
else
{
// Blue is max
h = XMVectorDivide(XMVectorSubtract(r, g), d);
h = XMVectorAdd(h, g_XMFour);
}
h = XMVectorDivide(h, g_XMSix);
XMVECTOR hv = XMVectorSelect(v, h, g_XMSelect1000);
XMVECTOR hva = XMVectorSelect(rgb, hv, g_XMSelect1110);
return XMVectorSelect(s, hva, g_XMSelect1011);
}
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMColorHSVToRGB(FXMVECTOR hsv) noexcept
{
XMVECTOR h = XMVectorSplatX(hsv);
XMVECTOR s = XMVectorSplatY(hsv);
XMVECTOR v = XMVectorSplatZ(hsv);
XMVECTOR h6 = XMVectorMultiply(h, g_XMSix);
XMVECTOR i = XMVectorFloor(h6);
XMVECTOR f = XMVectorSubtract(h6, i);
// p = v* (1-s)
XMVECTOR p = XMVectorMultiply(v, XMVectorSubtract(g_XMOne, s));
// q = v*(1-f*s)
XMVECTOR q = XMVectorMultiply(v, XMVectorSubtract(g_XMOne, XMVectorMultiply(f, s)));
// t = v*(1 - (1-f)*s)
XMVECTOR t = XMVectorMultiply(v, XMVectorSubtract(g_XMOne, XMVectorMultiply(XMVectorSubtract(g_XMOne, f), s)));
auto ii = static_cast<int>(XMVectorGetX(XMVectorMod(i, g_XMSix)));
XMVECTOR _rgb;
switch (ii)
{
case 0: // rgb = vtp
{
XMVECTOR vt = XMVectorSelect(t, v, g_XMSelect1000);
_rgb = XMVectorSelect(p, vt, g_XMSelect1100);
}
break;
case 1: // rgb = qvp
{
XMVECTOR qv = XMVectorSelect(v, q, g_XMSelect1000);
_rgb = XMVectorSelect(p, qv, g_XMSelect1100);
}
break;
case 2: // rgb = pvt
{
XMVECTOR pv = XMVectorSelect(v, p, g_XMSelect1000);
_rgb = XMVectorSelect(t, pv, g_XMSelect1100);
}
break;
case 3: // rgb = pqv
{
XMVECTOR pq = XMVectorSelect(q, p, g_XMSelect1000);
_rgb = XMVectorSelect(v, pq, g_XMSelect1100);
}
break;
case 4: // rgb = tpv
{
XMVECTOR tp = XMVectorSelect(p, t, g_XMSelect1000);
_rgb = XMVectorSelect(v, tp, g_XMSelect1100);
}
break;
default: // rgb = vpq
{
XMVECTOR vp = XMVectorSelect(p, v, g_XMSelect1000);
_rgb = XMVectorSelect(q, vp, g_XMSelect1100);
}
break;
}
return XMVectorSelect(hsv, _rgb, g_XMSelect1110);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMColorRGBToYUV(FXMVECTOR rgb) noexcept
{
static const XMVECTORF32 Scale0 = { { { 0.299f, -0.147f, 0.615f, 0.0f } } };
static const XMVECTORF32 Scale1 = { { { 0.587f, -0.289f, -0.515f, 0.0f } } };
static const XMVECTORF32 Scale2 = { { { 0.114f, 0.436f, -0.100f, 0.0f } } };
XMMATRIX M(Scale0, Scale1, Scale2, g_XMZero);
XMVECTOR clr = XMVector3Transform(rgb, M);
return XMVectorSelect(rgb, clr, g_XMSelect1110);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMColorYUVToRGB(FXMVECTOR yuv) noexcept
{
static const XMVECTORF32 Scale1 = { { { 0.0f, -0.395f, 2.032f, 0.0f } } };
static const XMVECTORF32 Scale2 = { { { 1.140f, -0.581f, 0.0f, 0.0f } } };
XMMATRIX M(g_XMOne, Scale1, Scale2, g_XMZero);
XMVECTOR clr = XMVector3Transform(yuv, M);
return XMVectorSelect(yuv, clr, g_XMSelect1110);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMColorRGBToYUV_HD(FXMVECTOR rgb) noexcept
{
static const XMVECTORF32 Scale0 = { { { 0.2126f, -0.0997f, 0.6150f, 0.0f } } };
static const XMVECTORF32 Scale1 = { { { 0.7152f, -0.3354f, -0.5586f, 0.0f } } };
static const XMVECTORF32 Scale2 = { { { 0.0722f, 0.4351f, -0.0564f, 0.0f } } };
XMMATRIX M(Scale0, Scale1, Scale2, g_XMZero);
XMVECTOR clr = XMVector3Transform(rgb, M);
return XMVectorSelect(rgb, clr, g_XMSelect1110);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMColorYUVToRGB_HD(FXMVECTOR yuv) noexcept
{
static const XMVECTORF32 Scale1 = { { { 0.0f, -0.2153f, 2.1324f, 0.0f } } };
static const XMVECTORF32 Scale2 = { { { 1.2803f, -0.3806f, 0.0f, 0.0f } } };
XMMATRIX M(g_XMOne, Scale1, Scale2, g_XMZero);
XMVECTOR clr = XMVector3Transform(yuv, M);
return XMVectorSelect(yuv, clr, g_XMSelect1110);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMColorRGBToYUV_UHD(FXMVECTOR rgb) noexcept
{
static const XMVECTORF32 Scale0 = { { { 0.2627f, -0.1215f, 0.6150f, 0.0f } } };
static const XMVECTORF32 Scale1 = { { { 0.6780f, -0.3136f, -0.5655f, 0.0f } } };
static const XMVECTORF32 Scale2 = { { { 0.0593f, 0.4351f, -0.0495f, 0.0f } } };
XMMATRIX M(Scale0, Scale1, Scale2, g_XMZero);
XMVECTOR clr = XMVector3Transform(rgb, M);
return XMVectorSelect(rgb, clr, g_XMSelect1110);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMColorYUVToRGB_UHD(FXMVECTOR yuv) noexcept
{
static const XMVECTORF32 Scale1 = { { { 0.0f, -0.1891f, 2.1620f, 0.0f } } };
static const XMVECTORF32 Scale2 = { { { 1.1989f, -0.4645f, 0.0f, 0.0f } } };
XMMATRIX M(g_XMOne, Scale1, Scale2, g_XMZero);
XMVECTOR clr = XMVector3Transform(yuv, M);
return XMVectorSelect(yuv, clr, g_XMSelect1110);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMColorRGBToXYZ(FXMVECTOR rgb) noexcept
{
static const XMVECTORF32 Scale0 = { { { 0.4887180f, 0.1762044f, 0.0000000f, 0.0f } } };
static const XMVECTORF32 Scale1 = { { { 0.3106803f, 0.8129847f, 0.0102048f, 0.0f } } };
static const XMVECTORF32 Scale2 = { { { 0.2006017f, 0.0108109f, 0.9897952f, 0.0f } } };
static const XMVECTORF32 Scale = { { { 1.f / 0.17697f, 1.f / 0.17697f, 1.f / 0.17697f, 0.0f } } };
XMMATRIX M(Scale0, Scale1, Scale2, g_XMZero);
XMVECTOR clr = XMVectorMultiply(XMVector3Transform(rgb, M), Scale);
return XMVectorSelect(rgb, clr, g_XMSelect1110);
}
inline XMVECTOR XM_CALLCONV XMColorXYZToRGB(FXMVECTOR xyz) noexcept
{
static const XMVECTORF32 Scale0 = { { { 2.3706743f, -0.5138850f, 0.0052982f, 0.0f } } };
static const XMVECTORF32 Scale1 = { { { -0.9000405f, 1.4253036f, -0.0146949f, 0.0f } } };
static const XMVECTORF32 Scale2 = { { { -0.4706338f, 0.0885814f, 1.0093968f, 0.0f } } };
static const XMVECTORF32 Scale = { { { 0.17697f, 0.17697f, 0.17697f, 0.0f } } };
XMMATRIX M(Scale0, Scale1, Scale2, g_XMZero);
XMVECTOR clr = XMVector3Transform(XMVectorMultiply(xyz, Scale), M);
return XMVectorSelect(xyz, clr, g_XMSelect1110);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMColorXYZToSRGB(FXMVECTOR xyz) noexcept
{
static const XMVECTORF32 Scale0 = { { { 3.2406f, -0.9689f, 0.0557f, 0.0f } } };
static const XMVECTORF32 Scale1 = { { { -1.5372f, 1.8758f, -0.2040f, 0.0f } } };
static const XMVECTORF32 Scale2 = { { { -0.4986f, 0.0415f, 1.0570f, 0.0f } } };
static const XMVECTORF32 Cutoff = { { { 0.0031308f, 0.0031308f, 0.0031308f, 0.0f } } };
static const XMVECTORF32 Exp = { { { 1.0f / 2.4f, 1.0f / 2.4f, 1.0f / 2.4f, 1.0f } } };
XMMATRIX M(Scale0, Scale1, Scale2, g_XMZero);
XMVECTOR lclr = XMVector3Transform(xyz, M);
XMVECTOR sel = XMVectorGreater(lclr, Cutoff);
// clr = 12.92 * lclr for lclr <= 0.0031308f
XMVECTOR smallC = XMVectorMultiply(lclr, g_XMsrgbScale);
// clr = (1+a)*pow(lclr, 1/2.4) - a for lclr > 0.0031308 (where a = 0.055)
XMVECTOR largeC = XMVectorSubtract(XMVectorMultiply(g_XMsrgbA1, XMVectorPow(lclr, Exp)), g_XMsrgbA);
XMVECTOR clr = XMVectorSelect(smallC, largeC, sel);
return XMVectorSelect(xyz, clr, g_XMSelect1110);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMColorSRGBToXYZ(FXMVECTOR srgb) noexcept
{
static const XMVECTORF32 Scale0 = { { { 0.4124f, 0.2126f, 0.0193f, 0.0f } } };
static const XMVECTORF32 Scale1 = { { { 0.3576f, 0.7152f, 0.1192f, 0.0f } } };
static const XMVECTORF32 Scale2 = { { { 0.1805f, 0.0722f, 0.9505f, 0.0f } } };
static const XMVECTORF32 Cutoff = { { { 0.04045f, 0.04045f, 0.04045f, 0.0f } } };
static const XMVECTORF32 Exp = { { { 2.4f, 2.4f, 2.4f, 1.0f } } };
XMVECTOR sel = XMVectorGreater(srgb, Cutoff);
// lclr = clr / 12.92
XMVECTOR smallC = XMVectorDivide(srgb, g_XMsrgbScale);
// lclr = pow( (clr + a) / (1+a), 2.4 )
XMVECTOR largeC = XMVectorPow(XMVectorDivide(XMVectorAdd(srgb, g_XMsrgbA), g_XMsrgbA1), Exp);
XMVECTOR lclr = XMVectorSelect(smallC, largeC, sel);
XMMATRIX M(Scale0, Scale1, Scale2, g_XMZero);
XMVECTOR clr = XMVector3Transform(lclr, M);
return XMVectorSelect(srgb, clr, g_XMSelect1110);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMColorRGBToSRGB(FXMVECTOR rgb) noexcept
{
static const XMVECTORF32 Cutoff = { { { 0.0031308f, 0.0031308f, 0.0031308f, 1.f } } };
static const XMVECTORF32 Linear = { { { 12.92f, 12.92f, 12.92f, 1.f } } };
static const XMVECTORF32 Scale = { { { 1.055f, 1.055f, 1.055f, 1.f } } };
static const XMVECTORF32 Bias = { { { 0.055f, 0.055f, 0.055f, 0.f } } };
static const XMVECTORF32 InvGamma = { { { 1.0f / 2.4f, 1.0f / 2.4f, 1.0f / 2.4f, 1.f } } };
XMVECTOR V = XMVectorSaturate(rgb);
XMVECTOR V0 = XMVectorMultiply(V, Linear);
XMVECTOR V1 = XMVectorSubtract(XMVectorMultiply(Scale, XMVectorPow(V, InvGamma)), Bias);
XMVECTOR select = XMVectorLess(V, Cutoff);
V = XMVectorSelect(V1, V0, select);
return XMVectorSelect(rgb, V, g_XMSelect1110);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMColorSRGBToRGB(FXMVECTOR srgb) noexcept
{
static const XMVECTORF32 Cutoff = { { { 0.04045f, 0.04045f, 0.04045f, 1.f } } };
static const XMVECTORF32 ILinear = { { { 1.f / 12.92f, 1.f / 12.92f, 1.f / 12.92f, 1.f } } };
static const XMVECTORF32 Scale = { { { 1.f / 1.055f, 1.f / 1.055f, 1.f / 1.055f, 1.f } } };
static const XMVECTORF32 Bias = { { { 0.055f, 0.055f, 0.055f, 0.f } } };
static const XMVECTORF32 Gamma = { { { 2.4f, 2.4f, 2.4f, 1.f } } };
XMVECTOR V = XMVectorSaturate(srgb);
XMVECTOR V0 = XMVectorMultiply(V, ILinear);
XMVECTOR V1 = XMVectorPow(XMVectorMultiply(XMVectorAdd(V, Bias), Scale), Gamma);
XMVECTOR select = XMVectorGreater(V, Cutoff);
V = XMVectorSelect(V0, V1, select);
return XMVectorSelect(srgb, V, g_XMSelect1110);
}
/****************************************************************************
*
* Miscellaneous
*
****************************************************************************/
//------------------------------------------------------------------------------
inline bool XMVerifyCPUSupport() noexcept
{
#if defined(_XM_SSE_INTRINSICS_) && !defined(_XM_NO_INTRINSICS_)
int CPUInfo[4] = { -1 };
#if defined(__clang__) || defined(__GNUC__)
__cpuid(0, CPUInfo[0], CPUInfo[1], CPUInfo[2], CPUInfo[3]);
#else
__cpuid(CPUInfo, 0);
#endif
#ifdef __AVX2__
if (CPUInfo[0] < 7)
return false;
#else
if (CPUInfo[0] < 1)
return false;
#endif
#if defined(__clang__) || defined(__GNUC__)
__cpuid(1, CPUInfo[0], CPUInfo[1], CPUInfo[2], CPUInfo[3]);
#else
__cpuid(CPUInfo, 1);
#endif
#if defined(__AVX2__) || defined(_XM_AVX2_INTRINSICS_)
// The compiler can emit FMA3 instructions even without explicit intrinsics use
if ((CPUInfo[2] & 0x38081001) != 0x38081001)
return false; // No F16C/AVX/OSXSAVE/SSE4.1/FMA3/SSE3 support
#elif defined(_XM_FMA3_INTRINSICS_) && defined(_XM_F16C_INTRINSICS_)
if ((CPUInfo[2] & 0x38081001) != 0x38081001)
return false; // No F16C/AVX/OSXSAVE/SSE4.1/FMA3/SSE3 support
#elif defined(_XM_FMA3_INTRINSICS_)
if ((CPUInfo[2] & 0x18081001) != 0x18081001)
return false; // No AVX/OSXSAVE/SSE4.1/FMA3/SSE3 support
#elif defined(_XM_F16C_INTRINSICS_)
if ((CPUInfo[2] & 0x38080001) != 0x38080001)
return false; // No F16C/AVX/OSXSAVE/SSE4.1/SSE3 support
#elif defined(__AVX__) || defined(_XM_AVX_INTRINSICS_)
if ((CPUInfo[2] & 0x18080001) != 0x18080001)
return false; // No AVX/OSXSAVE/SSE4.1/SSE3 support
#elif defined(_XM_SSE4_INTRINSICS_)
if ((CPUInfo[2] & 0x80001) != 0x80001)
return false; // No SSE3/SSE4.1 support
#elif defined(_XM_SSE3_INTRINSICS_)
if (!(CPUInfo[2] & 0x1))
return false; // No SSE3 support
#endif
// The x64 processor model requires SSE2 support, but no harm in checking
if ((CPUInfo[3] & 0x6000000) != 0x6000000)
return false; // No SSE2/SSE support
#if defined(__AVX2__) || defined(_XM_AVX2_INTRINSICS_)
#if defined(__clang__) || defined(__GNUC__)
__cpuid_count(7, 0, CPUInfo[0], CPUInfo[1], CPUInfo[2], CPUInfo[3]);
#else
__cpuidex(CPUInfo, 7, 0);
#endif
if (!(CPUInfo[1] & 0x20))
return false; // No AVX2 support
#endif
return true;
#elif defined(_XM_ARM_NEON_INTRINSICS_) && !defined(_XM_NO_INTRINSICS_)
// ARM-NEON support is required for the Windows on ARM platform
return true;
#else
// No intrinsics path always supported
return true;
#endif
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMFresnelTerm
(
FXMVECTOR CosIncidentAngle,
FXMVECTOR RefractionIndex
) noexcept
{
assert(!XMVector4IsInfinite(CosIncidentAngle));
// Result = 0.5f * (g - c)^2 / (g + c)^2 * ((c * (g + c) - 1)^2 / (c * (g - c) + 1)^2 + 1) where
// c = CosIncidentAngle
// g = sqrt(c^2 + RefractionIndex^2 - 1)
#if defined(_XM_NO_INTRINSICS_) || defined(_XM_ARM_NEON_INTRINSICS_)
XMVECTOR G = XMVectorMultiplyAdd(RefractionIndex, RefractionIndex, g_XMNegativeOne.v);
G = XMVectorMultiplyAdd(CosIncidentAngle, CosIncidentAngle, G);
G = XMVectorAbs(G);
G = XMVectorSqrt(G);
XMVECTOR S = XMVectorAdd(G, CosIncidentAngle);
XMVECTOR D = XMVectorSubtract(G, CosIncidentAngle);
XMVECTOR V0 = XMVectorMultiply(D, D);
XMVECTOR V1 = XMVectorMultiply(S, S);
V1 = XMVectorReciprocal(V1);
V0 = XMVectorMultiply(g_XMOneHalf.v, V0);
V0 = XMVectorMultiply(V0, V1);
XMVECTOR V2 = XMVectorMultiplyAdd(CosIncidentAngle, S, g_XMNegativeOne.v);
XMVECTOR V3 = XMVectorMultiplyAdd(CosIncidentAngle, D, g_XMOne.v);
V2 = XMVectorMultiply(V2, V2);
V3 = XMVectorMultiply(V3, V3);
V3 = XMVectorReciprocal(V3);
V2 = XMVectorMultiplyAdd(V2, V3, g_XMOne.v);
XMVECTOR Result = XMVectorMultiply(V0, V2);
Result = XMVectorSaturate(Result);
return Result;
#elif defined(_XM_SSE_INTRINSICS_)
// G = sqrt(abs((RefractionIndex^2-1) + CosIncidentAngle^2))
XMVECTOR G = _mm_mul_ps(RefractionIndex, RefractionIndex);
XMVECTOR vTemp = _mm_mul_ps(CosIncidentAngle, CosIncidentAngle);
G = _mm_sub_ps(G, g_XMOne);
vTemp = _mm_add_ps(vTemp, G);
// max((0-vTemp),vTemp) == abs(vTemp)
// The abs is needed to deal with refraction and cosine being zero
G = _mm_setzero_ps();
G = _mm_sub_ps(G, vTemp);
G = _mm_max_ps(G, vTemp);
// Last operation, the sqrt()
G = _mm_sqrt_ps(G);
// Calc G-C and G+C
XMVECTOR GAddC = _mm_add_ps(G, CosIncidentAngle);
XMVECTOR GSubC = _mm_sub_ps(G, CosIncidentAngle);
// Perform the term (0.5f *(g - c)^2) / (g + c)^2
XMVECTOR vResult = _mm_mul_ps(GSubC, GSubC);
vTemp = _mm_mul_ps(GAddC, GAddC);
vResult = _mm_mul_ps(vResult, g_XMOneHalf);
vResult = _mm_div_ps(vResult, vTemp);
// Perform the term ((c * (g + c) - 1)^2 / (c * (g - c) + 1)^2 + 1)
GAddC = _mm_mul_ps(GAddC, CosIncidentAngle);
GSubC = _mm_mul_ps(GSubC, CosIncidentAngle);
GAddC = _mm_sub_ps(GAddC, g_XMOne);
GSubC = _mm_add_ps(GSubC, g_XMOne);
GAddC = _mm_mul_ps(GAddC, GAddC);
GSubC = _mm_mul_ps(GSubC, GSubC);
GAddC = _mm_div_ps(GAddC, GSubC);
GAddC = _mm_add_ps(GAddC, g_XMOne);
// Multiply the two term parts
vResult = _mm_mul_ps(vResult, GAddC);
// Clamp to 0.0 - 1.0f
vResult = _mm_max_ps(vResult, g_XMZero);
vResult = _mm_min_ps(vResult, g_XMOne);
return vResult;
#endif
}
//------------------------------------------------------------------------------
inline bool XMScalarNearEqual
(
float S1,
float S2,
float Epsilon
) noexcept
{
float Delta = S1 - S2;
return (fabsf(Delta) <= Epsilon);
}
//------------------------------------------------------------------------------
// Modulo the range of the given angle such that -XM_PI <= Angle < XM_PI
inline float XMScalarModAngle(float Angle) noexcept
{
// Note: The modulo is performed with unsigned math only to work
// around a precision error on numbers that are close to PI
// Normalize the range from 0.0f to XM_2PI
Angle = Angle + XM_PI;
// Perform the modulo, unsigned
float fTemp = fabsf(Angle);
fTemp = fTemp - (XM_2PI * static_cast<float>(static_cast<int32_t>(fTemp / XM_2PI)));
// Restore the number to the range of -XM_PI to XM_PI-epsilon
fTemp = fTemp - XM_PI;
// If the modulo'd value was negative, restore negation
if (Angle < 0.0f)
{
fTemp = -fTemp;
}
return fTemp;
}
//------------------------------------------------------------------------------
inline float XMScalarSin(float Value) noexcept
{
// Map Value to y in [-pi,pi], x = 2*pi*quotient + remainder.
float quotient = XM_1DIV2PI * Value;
if (Value >= 0.0f)
{
quotient = static_cast<float>(static_cast<int>(quotient + 0.5f));
}
else
{
quotient = static_cast<float>(static_cast<int>(quotient - 0.5f));
}
float y = Value - XM_2PI * quotient;
// Map y to [-pi/2,pi/2] with sin(y) = sin(Value).
if (y > XM_PIDIV2)
{
y = XM_PI - y;
}
else if (y < -XM_PIDIV2)
{
y = -XM_PI - y;
}
// 11-degree minimax approximation
float y2 = y * y;
return (((((-2.3889859e-08f * y2 + 2.7525562e-06f) * y2 - 0.00019840874f) * y2 + 0.0083333310f) * y2 - 0.16666667f) * y2 + 1.0f) * y;
}
//------------------------------------------------------------------------------
inline float XMScalarSinEst(float Value) noexcept
{
// Map Value to y in [-pi,pi], x = 2*pi*quotient + remainder.
float quotient = XM_1DIV2PI * Value;
if (Value >= 0.0f)
{
quotient = static_cast<float>(static_cast<int>(quotient + 0.5f));
}
else
{
quotient = static_cast<float>(static_cast<int>(quotient - 0.5f));
}
float y = Value - XM_2PI * quotient;
// Map y to [-pi/2,pi/2] with sin(y) = sin(Value).
if (y > XM_PIDIV2)
{
y = XM_PI - y;
}
else if (y < -XM_PIDIV2)
{
y = -XM_PI - y;
}
// 7-degree minimax approximation
float y2 = y * y;
return (((-0.00018524670f * y2 + 0.0083139502f) * y2 - 0.16665852f) * y2 + 1.0f) * y;
}
//------------------------------------------------------------------------------
inline float XMScalarCos(float Value) noexcept
{
// Map Value to y in [-pi,pi], x = 2*pi*quotient + remainder.
float quotient = XM_1DIV2PI * Value;
if (Value >= 0.0f)
{
quotient = static_cast<float>(static_cast<int>(quotient + 0.5f));
}
else
{
quotient = static_cast<float>(static_cast<int>(quotient - 0.5f));
}
float y = Value - XM_2PI * quotient;
// Map y to [-pi/2,pi/2] with cos(y) = sign*cos(x).
float sign;
if (y > XM_PIDIV2)
{
y = XM_PI - y;
sign = -1.0f;
}
else if (y < -XM_PIDIV2)
{
y = -XM_PI - y;
sign = -1.0f;
}
else
{
sign = +1.0f;
}
// 10-degree minimax approximation
float y2 = y * y;
float p = ((((-2.6051615e-07f * y2 + 2.4760495e-05f) * y2 - 0.0013888378f) * y2 + 0.041666638f) * y2 - 0.5f) * y2 + 1.0f;
return sign * p;
}
//------------------------------------------------------------------------------
inline float XMScalarCosEst(float Value) noexcept
{
// Map Value to y in [-pi,pi], x = 2*pi*quotient + remainder.
float quotient = XM_1DIV2PI * Value;
if (Value >= 0.0f)
{
quotient = static_cast<float>(static_cast<int>(quotient + 0.5f));
}
else
{
quotient = static_cast<float>(static_cast<int>(quotient - 0.5f));
}
float y = Value - XM_2PI * quotient;
// Map y to [-pi/2,pi/2] with cos(y) = sign*cos(x).
float sign;
if (y > XM_PIDIV2)
{
y = XM_PI - y;
sign = -1.0f;
}
else if (y < -XM_PIDIV2)
{
y = -XM_PI - y;
sign = -1.0f;
}
else
{
sign = +1.0f;
}
// 6-degree minimax approximation
float y2 = y * y;
float p = ((-0.0012712436f * y2 + 0.041493919f) * y2 - 0.49992746f) * y2 + 1.0f;
return sign * p;
}
//------------------------------------------------------------------------------
_Use_decl_annotations_
inline void XMScalarSinCos
(
float* pSin,
float* pCos,
float Value
) noexcept
{
assert(pSin);
assert(pCos);
// Map Value to y in [-pi,pi], x = 2*pi*quotient + remainder.
float quotient = XM_1DIV2PI * Value;
if (Value >= 0.0f)
{
quotient = static_cast<float>(static_cast<int>(quotient + 0.5f));
}
else
{
quotient = static_cast<float>(static_cast<int>(quotient - 0.5f));
}
float y = Value - XM_2PI * quotient;
// Map y to [-pi/2,pi/2] with sin(y) = sin(Value).
float sign;
if (y > XM_PIDIV2)
{
y = XM_PI - y;
sign = -1.0f;
}
else if (y < -XM_PIDIV2)
{
y = -XM_PI - y;
sign = -1.0f;
}
else
{
sign = +1.0f;
}
float y2 = y * y;
// 11-degree minimax approximation
*pSin = (((((-2.3889859e-08f * y2 + 2.7525562e-06f) * y2 - 0.00019840874f) * y2 + 0.0083333310f) * y2 - 0.16666667f) * y2 + 1.0f) * y;
// 10-degree minimax approximation
float p = ((((-2.6051615e-07f * y2 + 2.4760495e-05f) * y2 - 0.0013888378f) * y2 + 0.041666638f) * y2 - 0.5f) * y2 + 1.0f;
*pCos = sign * p;
}
//------------------------------------------------------------------------------
_Use_decl_annotations_
inline void XMScalarSinCosEst
(
float* pSin,
float* pCos,
float Value
) noexcept
{
assert(pSin);
assert(pCos);
// Map Value to y in [-pi,pi], x = 2*pi*quotient + remainder.
float quotient = XM_1DIV2PI * Value;
if (Value >= 0.0f)
{
quotient = static_cast<float>(static_cast<int>(quotient + 0.5f));
}
else
{
quotient = static_cast<float>(static_cast<int>(quotient - 0.5f));
}
float y = Value - XM_2PI * quotient;
// Map y to [-pi/2,pi/2] with sin(y) = sin(Value).
float sign;
if (y > XM_PIDIV2)
{
y = XM_PI - y;
sign = -1.0f;
}
else if (y < -XM_PIDIV2)
{
y = -XM_PI - y;
sign = -1.0f;
}
else
{
sign = +1.0f;
}
float y2 = y * y;
// 7-degree minimax approximation
*pSin = (((-0.00018524670f * y2 + 0.0083139502f) * y2 - 0.16665852f) * y2 + 1.0f) * y;
// 6-degree minimax approximation
float p = ((-0.0012712436f * y2 + 0.041493919f) * y2 - 0.49992746f) * y2 + 1.0f;
*pCos = sign * p;
}
//------------------------------------------------------------------------------
inline float XMScalarASin(float Value) noexcept
{
// Clamp input to [-1,1].
bool nonnegative = (Value >= 0.0f);
float x = fabsf(Value);
float omx = 1.0f - x;
if (omx < 0.0f)
{
omx = 0.0f;
}
float root = sqrtf(omx);
// 7-degree minimax approximation
float result = ((((((-0.0012624911f * x + 0.0066700901f) * x - 0.0170881256f) * x + 0.0308918810f) * x - 0.0501743046f) * x + 0.0889789874f) * x - 0.2145988016f) * x + 1.5707963050f;
result *= root; // acos(|x|)
// acos(x) = pi - acos(-x) when x < 0, asin(x) = pi/2 - acos(x)
return (nonnegative ? XM_PIDIV2 - result : result - XM_PIDIV2);
}
//------------------------------------------------------------------------------
inline float XMScalarASinEst(float Value) noexcept
{
// Clamp input to [-1,1].
bool nonnegative = (Value >= 0.0f);
float x = fabsf(Value);
float omx = 1.0f - x;
if (omx < 0.0f)
{
omx = 0.0f;
}
float root = sqrtf(omx);
// 3-degree minimax approximation
float result = ((-0.0187293f * x + 0.0742610f) * x - 0.2121144f) * x + 1.5707288f;
result *= root; // acos(|x|)
// acos(x) = pi - acos(-x) when x < 0, asin(x) = pi/2 - acos(x)
return (nonnegative ? XM_PIDIV2 - result : result - XM_PIDIV2);
}
//------------------------------------------------------------------------------
inline float XMScalarACos(float Value) noexcept
{
// Clamp input to [-1,1].
bool nonnegative = (Value >= 0.0f);
float x = fabsf(Value);
float omx = 1.0f - x;
if (omx < 0.0f)
{
omx = 0.0f;
}
float root = sqrtf(omx);
// 7-degree minimax approximation
float result = ((((((-0.0012624911f * x + 0.0066700901f) * x - 0.0170881256f) * x + 0.0308918810f) * x - 0.0501743046f) * x + 0.0889789874f) * x - 0.2145988016f) * x + 1.5707963050f;
result *= root;
// acos(x) = pi - acos(-x) when x < 0
return (nonnegative ? result : XM_PI - result);
}
//------------------------------------------------------------------------------
inline float XMScalarACosEst(float Value) noexcept
{
// Clamp input to [-1,1].
bool nonnegative = (Value >= 0.0f);
float x = fabsf(Value);
float omx = 1.0f - x;
if (omx < 0.0f)
{
omx = 0.0f;
}
float root = sqrtf(omx);
// 3-degree minimax approximation
float result = ((-0.0187293f * x + 0.0742610f) * x - 0.2121144f) * x + 1.5707288f;
result *= root;
// acos(x) = pi - acos(-x) when x < 0
return (nonnegative ? result : XM_PI - result);
}
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