Refactor trigonometric funcs, optimize GGX benchmark
- Replaced SIMD-based Sin/Cos/SinCos in WideLane with generic polynomial approximations for hardware independence. - Updated ScalarLane Cast to use CreateTruncating. - Applied AggressiveOptimization to key GGX methods; improved luma calculation and radical inverse LUT handling. - Enhanced GGX benchmark setup, cleanup, and timing logic. - Bumped project version to 1.3.1.
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@@ -578,58 +578,129 @@ public readonly unsafe partial struct WideLane<TNumber> : ISPMDLane<WideLane<TNu
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static WideLane<TNumber> Sin(WideLane<TNumber> value)
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{
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if (typeof(TNumber) == typeof(float))
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{
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ref var v = ref Unsafe.As<WideLane<TNumber>, Vector<float>>(ref value);
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var result = Vector.Sin(v);
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return new WideLane<TNumber>(Unsafe.As<Vector<float>, Vector<TNumber>>(ref result));
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}
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else if (typeof(TNumber) == typeof(double))
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{
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ref var v = ref Unsafe.As<WideLane<TNumber>, Vector<double>>(ref value);
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var result = Vector.Sin(v);
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return new WideLane<TNumber>(Unsafe.As<Vector<double>, Vector<TNumber>>(ref result));
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}
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var invPi = Create(TNumber.CreateTruncating(0.318309886f)); // 1 / PI
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return value;
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var x_sin = value;
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var y_sin = x_sin * invPi;
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var k_sin = Round(y_sin);
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var z_sin = y_sin - k_sin;
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var half = Create(TNumber.CreateTruncating(0.5f));
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var two = Create(TNumber.CreateTruncating(2.0f));
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var k_even_sin = Round(k_sin * half) * two;
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var sign_sin = One - two * Abs(k_sin - k_even_sin);
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var c1 = Create(TNumber.CreateTruncating(3.14159265f)); // PI
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var c3 = Create(TNumber.CreateTruncating(-5.16771278f)); // -PI^3 / 6
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var c5 = Create(TNumber.CreateTruncating(2.55016404f)); // PI^5 / 120
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var c7 = Create(TNumber.CreateTruncating(-0.59926453f)); // -PI^7 / 5040
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var c9 = Create(TNumber.CreateTruncating(0.08214589f)); // PI^9 / 362880
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var z2_sin = z_sin * z_sin;
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var poly_sin = MultipleAdd(z2_sin, c9, c7); // c7 + c9*z^2
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poly_sin = MultipleAdd(z2_sin, poly_sin, c5); // c5 + z^2*(...)
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poly_sin = MultipleAdd(z2_sin, poly_sin, c3); // c3 + z^2*(...)
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poly_sin = MultipleAdd(z2_sin, poly_sin, c1); // c1 + z^2*(...)
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poly_sin = z_sin * poly_sin; // z * (...)
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return poly_sin * sign_sin;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static WideLane<TNumber> Cos(WideLane<TNumber> value)
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{
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if (typeof(TNumber) == typeof(float))
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{
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ref var v = ref Unsafe.As<WideLane<TNumber>, Vector<float>>(ref value);
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var result = Vector.Cos(v);
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return new WideLane<TNumber>(Unsafe.As<Vector<float>, Vector<TNumber>>(ref result));
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}
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else if (typeof(TNumber) == typeof(double))
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{
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ref var v = ref Unsafe.As<WideLane<TNumber>, Vector<double>>(ref value);
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var result = Vector.Cos(v);
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return new WideLane<TNumber>(Unsafe.As<Vector<double>, Vector<TNumber>>(ref result));
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}
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var halfPi = Create(TNumber.CreateTruncating(1.570796327f));
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var invPi = Create(TNumber.CreateTruncating(0.318309886f)); // 1 / PI
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return value;
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var x_cos = value + halfPi;
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var y_cos = x_cos * invPi;
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var k_cos = Round(y_cos);
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var z_cos = y_cos - k_cos;
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var half = Create(TNumber.CreateTruncating(0.5f));
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var two = Create(TNumber.CreateTruncating(2.0f));
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var k_even_cos = Round(k_cos * half) * two;
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var sign_cos = One - two * Abs(k_cos - k_even_cos);
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var c1 = Create(TNumber.CreateTruncating(3.14159265f)); // PI
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var c3 = Create(TNumber.CreateTruncating(-5.16771278f)); // -PI^3 / 6
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var c5 = Create(TNumber.CreateTruncating(2.55016404f)); // PI^5 / 120
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var c7 = Create(TNumber.CreateTruncating(-0.59926453f)); // -PI^7 / 5040
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var c9 = Create(TNumber.CreateTruncating(0.08214589f)); // PI^9 / 362880
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var z2_cos = z_cos * z_cos;
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var poly_cos = MultipleAdd(z2_cos, c9, c7);
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poly_cos = MultipleAdd(z2_cos, poly_cos, c5);
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poly_cos = MultipleAdd(z2_cos, poly_cos, c3);
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poly_cos = MultipleAdd(z2_cos, poly_cos, c1);
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poly_cos = z_cos * poly_cos;
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return poly_cos * sign_cos;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static (WideLane<TNumber> sin, WideLane<TNumber> cos) SinCos(WideLane<TNumber> value)
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{
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if (typeof(TNumber) == typeof(float))
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{
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ref var v = ref Unsafe.As<WideLane<TNumber>, Vector<float>>(ref value);
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var (sin, cos) = Vector.SinCos(v);
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return (new WideLane<TNumber>(Unsafe.As<Vector<float>, Vector<TNumber>>(ref sin)), new WideLane<TNumber>(Unsafe.As<Vector<float>, Vector<TNumber>>(ref cos)));
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}
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else if (typeof(TNumber) == typeof(double))
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{
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ref var v = ref Unsafe.As<WideLane<TNumber>, Vector<double>>(ref value);
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var (sin, cos) = Vector.SinCos(v);
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return (new WideLane<TNumber>(Unsafe.As<Vector<double>, Vector<TNumber>>(ref sin)), new WideLane<TNumber>(Unsafe.As<Vector<double>, Vector<TNumber>>(ref cos)));
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}
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var halfPi = Create(TNumber.CreateTruncating(1.570796327f));
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var invPi = Create(TNumber.CreateTruncating(0.318309886f)); // 1 / PI
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return (value, value);
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var x_sin = value;
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var x_cos = value + halfPi;
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// Range Reduction
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// We map any angle to the interval [-0.5, 0.5] (corresponding to the actual angle range [-PI/2, PI/2])
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// y = x * (1 / PI)
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var y_sin = x_sin * invPi;
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var y_cos = x_cos * invPi;
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// k = Round(y)
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var k_sin = Round(y_sin);
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var k_cos = Round(y_cos);
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// z = y - k (Now, the range of z is perfectly reduced to [-0.5, 0.5])
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var z_sin = y_sin - k_sin;
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var z_cos = y_cos - k_cos;
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// 2. Branchless Sign Flip
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// Mathematical principle: Sin(x + k*PI) = Sin(x) * (-1)^k
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// We need to compute (-1)^k. To avoid inefficient bit operations or branches, we compute it with floating-point math:
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// sign = 1.0 - 2.0 * Abs(k - 2.0 * Round(k * 0.5))
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var half = Create(TNumber.CreateTruncating(0.5f));
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var two = Create(TNumber.CreateTruncating(2.0f));
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var one = One;
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var k_even_sin = Round(k_sin * half) * two;
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var sign_sin = one - two * Abs(k_sin - k_even_sin);
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var k_even_cos = Round(k_cos * half) * two;
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var sign_cos = one - two * Abs(k_cos - k_even_cos);
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// 3. Taylor/Remez Polynomial for Sin(PI * z)
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// For z in [-0.5, 0.5]，Calculate sin(PI * z)
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// z * (C1 + z^2 * (C3 + z^2 * (C5 + z^2 * (C7 + z^2 * C9))))
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var c1 = Create(TNumber.CreateTruncating(3.14159265f)); // PI
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var c3 = Create(TNumber.CreateTruncating(-5.16771278f)); // -PI^3 / 6
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var c5 = Create(TNumber.CreateTruncating(2.55016404f)); // PI^5 / 120
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var c7 = Create(TNumber.CreateTruncating(-0.59926453f)); // -PI^7 / 5040
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var c9 = Create(TNumber.CreateTruncating(0.08214589f)); // PI^9 / 362880
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var z2_sin = z_sin * z_sin;
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var poly_sin = MultipleAdd(z2_sin, c9, c7); // c7 + c9*z^2
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poly_sin = MultipleAdd(z2_sin, poly_sin, c5); // c5 + z^2*(...)
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poly_sin = MultipleAdd(z2_sin, poly_sin, c3); // c3 + z^2*(...)
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poly_sin = MultipleAdd(z2_sin, poly_sin, c1); // c1 + z^2*(...)
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poly_sin = z_sin * poly_sin; // z * (...)
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var z2_cos = z_cos * z_cos;
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var poly_cos = MultipleAdd(z2_cos, c9, c7);
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poly_cos = MultipleAdd(z2_cos, poly_cos, c5);
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poly_cos = MultipleAdd(z2_cos, poly_cos, c3);
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poly_cos = MultipleAdd(z2_cos, poly_cos, c1);
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poly_cos = z_cos * poly_cos;
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return (poly_sin * sign_sin, poly_cos * sign_cos);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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