# Mathematical expressions¶

DALI allows you to use regular Python arithmetic operations and other mathematical functions in the define_graph() method on the values that are returned from invoking other operators.

Same expressions can be used with Functional API.

The expressions that are used will be incorporated into the pipeline without needing to explicitly instantiate operators and will describe the element-wise operations on Tensors.

At least one of the inputs to the arithmetic expression must be returned by other DALI operator - that is a value of nvidia.dali.pipeline.DataNode representing a batch of tensors. The other input can be nvidia.dali.types.Constant() or regular Python value of type bool, int, or float. As the operations performed are element-wise, the shapes of all operands must match.

Note

If one of the operands is a batch of Tensors that represent scalars, the scalar values are broadcast to the other operand.

For details and examples see expressions tutorials.

## Type promotion rules¶

For operations that accept two (or more) arguments, type promotions apply. The resulting type is calculated in accordance to the table below.

Operand Type

Operand Type

Result Type

T

T

T

floatX

T

floatX

where T is not a float

floatX

floatY

floatZ

where Z = max(X, Y)

intX

intY

intZ

where Z = max(X, Y)

uintX

uintY

uintZ

where Z = max(X, Y)

intX

uintY

int2Y

if X <= Y

intX

uintY

intX

if X > Y

T stands for any one of the supported numerical types: bool, int8, int16, int32, int64, uint8, uint16, uint32, uint64, float32, and float64.

bool type is considered the smallest unsigned integer type and is treated as uint1 with respect to the table above.

Note

Type promotion is commutative.

For more than two arguments, the resulting type is calculated as a reduction from left to right - first calculating the result of operating on first two arguments, next between that intermediate result and the third argument and so on, until we have only the result type left.

## Supported arithmetic operations¶

Currently, DALI supports the following operations:

Unary arithmetic operators: +, -

Unary operators that implement __pos__(self) and __neg__(self). The result of a unary arithmetic operation always preserves the input type. Unary operators accept only TensorList inputs from other operators.

Return type

TensorList of the same type

Binary arithmetic operations: +, -, *, /, //

Binary operators that implement __add__, __sub__, __mul__, __truediv__ and __floordiv__ respectively.

The result of an arithmetic operation between two operands is described above, with the exception of /, the __truediv__ operation, which always returns float32 or float64 type.

Note

The only allowed arithmetic operation between two bool values is multiplication (*).

Return type

TensorList of the type that is calculated based on the type promotion rules.

Comparison operations: ==, !=, <, <=, >, >=

Comparison operations.

Return type

TensorList of bool type.

Bitwise binary operations: &, |, ^

The bitwise binary operations follow the same type promotion rules as arithmetic binary operations, but their inputs are restricted to integral types (including bool).

Note

A bitwise operation can be applied to two boolean inputs. Those operations can be used to emulate element-wise logical operations on Tensors.

Return type

TensorList of the type that is calculated based on the type promotion rules.

## Mathematical funcions¶

Similarly to arithmetic expressions, one can use selected mathematical functions in the Pipeline graph definition. They also accept nvidia.dali.pipeline.DataNode, nvidia.dali.types.Constant() or regular Python value of type bool, int, or float as arguments. At least one of the inputs must be the output of other DALI Operator.

nvidia.dali.math.clamp(value, lo, hi)

Produces a tensor of values from value clamped to the range [lo, hi].

Return type

TensorList of the type that is calculated based on the type promotion rules.

nvidia.dali.math.exp(value)

Fills the output with exponential of value. :rtype: TensorList of exp(value). If value is an integer, the result will be float, otherwise the type is preserved.

nvidia.dali.math.log(value)

Fills the output with logarithm (base-10) of value. :rtype: TensorList of log(value). If value is an integer, the result will be float, otherwise the type is preserved.

nvidia.dali.math.max(left, right)

Fills the output with maxima of corresponding values in left and right.

Return type

TensorList of the type that is calculated based on the type promotion rules.

nvidia.dali.math.min(left, right)

Fills the output with minima of corresponding values in left and right.

Return type

TensorList of the type that is calculated based on the type promotion rules.