class

DivBackward

DivBackward

source edit

Python wrappers

pylucid.ops.divfunction

Autograd node for element-wise division $y = a / b$ with NumPy broadcasting.

Saves both forward inputs because the quotient rule for $\partial L / \partial b$ requires both $a$ and $b$ . Broadcast-reduces each branch back to the original input shape via sum_to_shape inside BinaryKernel::apply.

Math

y = \frac{a}{b}, \qquad \frac{\partial L}{\partial a} = \frac{1}{b} \cdot \frac{\partial L}{\partial y}, \qquad \frac{\partial L}{\partial b} = -\frac{a}{b^2} \cdot \frac{\partial L}{\partial y}

Shape

Inputs follow NumPy broadcasting; output has the broadcasted shape. Each gradient is then reduced to the original input's shape.

See Also

AddBackward, SubBackward, MulBackward

Attributes

kSavesInputsbool

true (inherited default from BinaryKernel) — both forward inputs are retained for the quotient-rule backward pass.

schema_v1OpSchema

"div", schema version 1, AmpPolicy::Promote, deterministic.

Notes

CPU dispatch uses Accelerate vDSP_vdiv / vDSP_vdivD for F32 / F64. GPU dispatch uses MLX's broadcast-aware divide primitive. Division by zero follows IEEE-754 semantics (yields $\pm\infty$ or NaN); no explicit guard is inserted.

Static methods

static

dispatch

→Storage

int dispatch(backend::IBackend & be, const int & a, const int & b, const int & shape, Dtype dt)

source edit

Forward dispatch hook called by BinaryKernel::forward.

Parameters

bebackend::IBackend&

Active backend (CPU Accelerate or GPU MLX).

a, bconst Storage&

Operands already broadcast-expanded to shape.

shapeconst Shape&

Broadcasted output shape.

dtDtype

Promoted output dtype.

Returns

Storage

Output storage holding $a / b$ .

Methods

grad_formula

→std::pair<Storage, Storage>

int grad_formula(const int & grad_out)

source edit

Compute the storage-level gradients for both operands (quotient rule).

Math

\mathrm{dA} = \frac{1}{b} \odot \frac{\partial L}{\partial y}, \qquad \mathrm{dB} = -\frac{a}{b^2} \odot \frac{\partial L}{\partial y}

Parameters

grad_outconst Storage&

Upstream gradient at the broadcasted output shape.

Returns

std::pair<Storage, Storage>

(dA, dB) where dA = grad_out / b_broadcast and dB = -(grad_out * a_broadcast) / b_broadcast^2. Both still at output shape; BinaryKernel::apply performs the broadcast reduction.

Notes

The implementation materialises intermediates (b_sq, g_times_a, div_by_b_sq) explicitly so each transient storage can be released as soon as it is no longer needed.

grad_formula_impl

→std::pair<TensorImplPtr, TensorImplPtr>

int grad_formula_impl(const int & grad_out, const int & a, const int & b)

source edit

Graph-mode (TensorImpl) variant of the gradient.

Parameters

grad_outconst TensorImplPtr&

Upstream gradient node.

a, bconst TensorImplPtr&

Forward inputs, already broadcast-expanded to out_shape_ by BinaryKernel.

Returns

std::pair<TensorImplPtr, TensorImplPtr>

(grad_out / b, -grad_out * a / b^2).

class

DivBackward

DivBackward

source edit

Python wrappers

pylucid.ops.divfunction

Autograd node for element-wise division $y = a / b$ with NumPy broadcasting.

Math

y = \frac{a}{b}, \qquad \frac{\partial L}{\partial a} = \frac{1}{b} \cdot \frac{\partial L}{\partial y}, \qquad \frac{\partial L}{\partial b} = -\frac{a}{b^2} \cdot \frac{\partial L}{\partial y}

Shape

Inputs follow NumPy broadcasting; output has the broadcasted shape. Each gradient is then reduced to the original input's shape.

See Also

AddBackward, SubBackward, MulBackward

Attributes

kSavesInputsbool

true (inherited default from BinaryKernel) — both forward inputs are retained for the quotient-rule backward pass.

schema_v1OpSchema

"div", schema version 1, AmpPolicy::Promote, deterministic.

Notes

Static methods

static

dispatch

→Storage

int dispatch(backend::IBackend & be, const int & a, const int & b, const int & shape, Dtype dt)

source edit

Forward dispatch hook called by BinaryKernel::forward.

Parameters

bebackend::IBackend&

Active backend (CPU Accelerate or GPU MLX).

a, bconst Storage&

Operands already broadcast-expanded to shape.

shapeconst Shape&

Broadcasted output shape.

dtDtype

Promoted output dtype.

Returns

Storage

Output storage holding $a / b$ .

Methods

grad_formula

→std::pair<Storage, Storage>

int grad_formula(const int & grad_out)

source edit

Compute the storage-level gradients for both operands (quotient rule).

Math

\mathrm{dA} = \frac{1}{b} \odot \frac{\partial L}{\partial y}, \qquad \mathrm{dB} = -\frac{a}{b^2} \odot \frac{\partial L}{\partial y}

Parameters

grad_outconst Storage&

Upstream gradient at the broadcasted output shape.

Returns

std::pair<Storage, Storage>

(dA, dB) where dA = grad_out / b_broadcast and dB = -(grad_out * a_broadcast) / b_broadcast^2. Both still at output shape; BinaryKernel::apply performs the broadcast reduction.

Notes

The implementation materialises intermediates (b_sq, g_times_a, div_by_b_sq) explicitly so each transient storage can be released as soon as it is no longer needed.

grad_formula_impl

→std::pair<TensorImplPtr, TensorImplPtr>

int grad_formula_impl(const int & grad_out, const int & a, const int & b)

source edit

Graph-mode (TensorImpl) variant of the gradient.

Parameters

grad_outconst TensorImplPtr&

Upstream gradient node.

a, bconst TensorImplPtr&

Forward inputs, already broadcast-expanded to out_shape_ by BinaryKernel.

Returns

std::pair<TensorImplPtr, TensorImplPtr>

(grad_out / b, -grad_out * a / b^2).