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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.
syntax __differentiate_jvp : JVPDerivativeModifier;
// Custom JVP Function reference
__attributeTarget(FunctionDeclBase)
attribute_syntax [__custom_jvp(function)] : CustomJVPAttribute;
/// Interface to denote types as differentiable.
/// Allows for user-specified differential types as
/// well as automatic generation, for when the associated type
/// hasn't been declared explicitly.
/// Note that the requirements must currently be defined in this exact order
/// since the auto-diff pass relies on the order to grab the struct keys.
///
__magic_type(DifferentiableType)
interface IDifferentiable
{
// Note: the compiler implementation requires the `Differential` associated type to be defined
// before anything else.
[__BuiltinRequirement(_BuiltinRequirementKind.DifferentialType)]
associatedtype Differential;
[__BuiltinRequirement(_BuiltinRequirementKind.DZeroFunc)]
static Differential zero();
[__BuiltinRequirement(_BuiltinRequirementKind.DAddFunc)]
static Differential dadd(Differential, Differential);
[__BuiltinRequirement(_BuiltinRequirementKind.DMulFunc)]
static Differential dmul(This, Differential);
};
// Add extensions for the standard types
extension float : IDifferentiable
{
typedef float Differential;
[__unsafeForceInlineEarly]
static Differential zero()
{
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;
}
}
extension vector<float, 3> : IDifferentiable
{
typedef vector<float, 3> Differential;
[__unsafeForceInlineEarly]
static Differential zero()
{
return vector<float, 3>(0.f);
}
[__unsafeForceInlineEarly]
static Differential dadd(Differential a, Differential b)
{
return a + b;
}
[__unsafeForceInlineEarly]
static Differential dmul(This a, Differential b)
{
return a * b;
}
}
extension vector<float, 2> : IDifferentiable
{
typedef vector<float, 2> Differential;
[__unsafeForceInlineEarly]
static Differential zero()
{
return vector<float, 2>(0.f);
}
[__unsafeForceInlineEarly]
static Differential dadd(Differential a, Differential b)
{
return a + b;
}
[__unsafeForceInlineEarly]
static Differential dmul(This a, Differential b)
{
return a * b;
}
}
extension vector<float, 4> : IDifferentiable
{
typedef vector<float, 4> Differential;
[__unsafeForceInlineEarly]
static Differential zero()
{
return vector<float, 4>(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($(kIROp_DifferentialPairType))
struct __DifferentialPair
{
__intrinsic_op($(kIROp_MakeDifferentialPair))
__init(T _primal, T.Differential _differential);
__intrinsic_op($(kIROp_DifferentialPairGetDifferential))
T.Differential d();
T.Differential getDifferential()
{
return d();
}
__intrinsic_op($(kIROp_DifferentialPairGetPrimal))
T p();
T getPrimal()
{
return p();
}
};
typealias IDFloat = IFloat & IDifferentiable;
namespace dstd
{
// Natural Exponent
__generic<T : IDFloat>
__target_intrinsic(hlsl)
__target_intrinsic(glsl)
__target_intrinsic(cuda, "$P_exp($0)")
__target_intrinsic(cpp, "$P_exp($0)")
__target_intrinsic(spirv_direct, "12 resultType resultId glsl450 27 _0")
[__custom_jvp(d_exp<T>)]
T exp(T x);
__generic<T : IDFloat>
__DifferentialPair<T> d_exp(__DifferentialPair<T> dpx)
{
return __DifferentialPair<T>(
exp(dpx.p()),
T.dmul(exp(dpx.p()), dpx.d()));
}
// Sine
__generic<T : IDFloat>
__target_intrinsic(hlsl)
__target_intrinsic(glsl)
__target_intrinsic(cuda, "$P_sin($0)")
__target_intrinsic(cpp, "$P_sin($0)")
__target_intrinsic(spirv_direct, "12 resultType resultId glsl450 13 _0")
[__custom_jvp(d_sin<T>)]
T sin(T x);
__generic<T : IDFloat>
__DifferentialPair<T> d_sin(__DifferentialPair<T> dpx)
{
return __DifferentialPair<T>(
sin(dpx.p()),
T.dmul(cos(dpx.p()), dpx.d()));
}
// Cosine
__generic<T : IDFloat>
__target_intrinsic(hlsl)
__target_intrinsic(glsl)
__target_intrinsic(cuda, "$P_cos($0)")
__target_intrinsic(cpp, "$P_cos($0)")
__target_intrinsic(spirv_direct, "12 resultType resultId glsl450 14 _0")
[__custom_jvp(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()));
}
};
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