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/// Modifer to mark a function for forward-mode differentiation.
/// i.e. the compiler will automatically generate a new function
/// that computes the jacobian-vector product of the original.
__attributeTarget(FunctionDeclBase)
attribute_syntax [ForwardDifferentiable] : ForwardDifferentiableAttribute;
// Custom Forward Derivative Function reference
__attributeTarget(FunctionDeclBase)
attribute_syntax [ForwardDerivative(function)] : ForwardDerivativeAttribute;
// Add extensions for the standard types
extension float : IDifferentiable
{
typedef float Differential;
[__unsafeForceInlineEarly]
static Differential dzero()
{
return float(0.f);
}
[__unsafeForceInlineEarly]
static Differential dadd(Differential a, Differential b)
{
return a + b;
}
[__unsafeForceInlineEarly]
static Differential dmul(This a, Differential b)
{
return a * b;
}
}
__generic<let N:int>
extension vector<float, N> : IDifferentiable
{
typedef vector<float, N> Differential;
[__unsafeForceInlineEarly]
static Differential dzero()
{
return vector<float, N>(0.f);
}
[__unsafeForceInlineEarly]
static Differential dadd(Differential a, Differential b)
{
return a + b;
}
[__unsafeForceInlineEarly]
static Differential dmul(This a, Differential b)
{
return a * b;
}
}
/// Pair type that serves to wrap the primal and
/// differential types of an arbitrary type T.
__generic<T : IDifferentiable>
__magic_type(DifferentialPairType)
__intrinsic_type($(kIROp_DifferentialPairType))
struct DifferentialPair : IDifferentiable
{
typedef DifferentialPair<T.Differential> Differential;
typedef T.Differential DifferentialElementType;
__intrinsic_op($(kIROp_MakeDifferentialPair))
__init(T _primal, T.Differential _differential);
property p : T
{
__intrinsic_op($(kIROp_DifferentialPairGetPrimal))
get;
}
property v : T
{
__intrinsic_op($(kIROp_DifferentialPairGetPrimal))
get;
}
property d : T.Differential
{
__intrinsic_op($(kIROp_DifferentialPairGetDifferential))
get;
}
[__unsafeForceInlineEarly]
T.Differential getDifferential()
{
return d;
}
[__unsafeForceInlineEarly]
T getPrimal()
{
return p;
}
[__unsafeForceInlineEarly]
static Differential dzero()
{
return Differential(T.dzero(), T.Differential.dzero());
}
[__unsafeForceInlineEarly]
static Differential dadd(Differential a, Differential b)
{
return Differential(
T.dadd(
a.p,
b.p
),
T.Differential.dadd(a.d, b.d));
}
[__unsafeForceInlineEarly]
static Differential dmul(This a, Differential b)
{
return Differential(
T.dmul(a.p, b.p),
T.Differential.dmul(a.d, b.d));
}
};
typealias IDFloat = IFloat & IDifferentiable;
#define VECTOR_MAP_UNARY(TYPE, COUNT, FUNC, VALUE) \
vector<TYPE,COUNT> result; for(int i = 0; i < COUNT; ++i) { result[i] = FUNC(VALUE[i]); } return result
namespace dstd
{
// Natural Exponent
__generic<T : IDFloat>
__target_intrinsic(hlsl)
__target_intrinsic(glsl)
__target_intrinsic(cuda, "$P_exp($0)")
__target_intrinsic(cpp, "$P_exp($0)")
__target_intrinsic(spirv_direct, "12 resultType resultId glsl450 27 _0")
[ForwardDerivative(d_exp<T>)]
T exp(T x);
__generic<T : IDFloat>
DifferentialPair<T> d_exp(DifferentialPair<T> dpx)
{
return DifferentialPair<T>(
exp(dpx.p),
T.dmul(exp(dpx.p), dpx.d));
}
// Sine
__generic<T : IDFloat>
__target_intrinsic(hlsl)
__target_intrinsic(glsl)
__target_intrinsic(cuda, "$P_sin($0)")
__target_intrinsic(cpp, "$P_sin($0)")
__target_intrinsic(spirv_direct, "12 resultType resultId glsl450 13 _0")
[ForwardDerivative(d_sin<T>)]
T sin(T x);
__generic<T : IDFloat>
DifferentialPair<T> d_sin(DifferentialPair<T> dpx)
{
return DifferentialPair<T>(
sin(dpx.p),
T.dmul(cos(dpx.p), dpx.d));
}
// Cosine
__generic<T : IDFloat>
__target_intrinsic(hlsl)
__target_intrinsic(glsl)
__target_intrinsic(cuda, "$P_cos($0)")
__target_intrinsic(cpp, "$P_cos($0)")
__target_intrinsic(spirv_direct, "12 resultType resultId glsl450 14 _0")
[ForwardDerivative(d_cos<T>)]
T cos(T x);
__generic<T : IDFloat>
DifferentialPair<T> d_cos(DifferentialPair<T> dpx)
{
return DifferentialPair<T>(
cos(dpx.p),
T.dmul(-sin(dpx.p), dpx.d));
}
__generic<let N : int>
__target_intrinsic(hlsl)
__target_intrinsic(glsl)
__target_intrinsic(spirv_direct, "12 resultType resultId glsl450 27 _0")
[ForwardDerivative(d_exp_vector)]
vector<float, N> exp(vector<float, N> x)
{
VECTOR_MAP_UNARY(float, N, dstd.exp, x);
}
__generic<let N : int>
DifferentialPair<vector<float, N>> d_exp_vector(DifferentialPair<vector<float, N>> dpx)
{
vector<float, N> result;
vector<float, N>.Differential d_result;
for(int i = 0; i < N; ++i)
{
DifferentialPair<float> dpexp = dstd.d_exp(DifferentialPair<float>(dpx.p[i], dpx.d[i]));
result[i] = dpexp.p;
d_result[i] = dpexp.d;
}
return DifferentialPair<vector<float, N>>(result, d_result);
}
};
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