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Basic operations

concrete_fhe_toolkit.math.basic

Basic bounded scalar operations for encrypted integers.

add 

add(left: Any, right: Any) -> Any

Compute the add of the inputs.

Parameters:

Name Type Description Default
left Any

The left encrypted operand.

 required
right Any

The right encrypted operand.

 required

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def add(left: Any, right: Any) -> Any:
    """Compute the add of the inputs.

        Args:
            left (Any): The left encrypted operand.
            right (Any): The right encrypted operand.

        Returns:
            Any: The result of the operation.
        """
    return left + right

subtract 

subtract(left: Any, right: Any) -> Any

Compute the subtract of the inputs.

Parameters:

Name Type Description Default
left Any

The left encrypted operand.

 required
right Any

The right encrypted operand.

 required

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def subtract(left: Any, right: Any) -> Any:
    """Compute the subtract of the inputs.

        Args:
            left (Any): The left encrypted operand.
            right (Any): The right encrypted operand.

        Returns:
            Any: The result of the operation.
        """
    return left - right

multiply 

multiply(left: Any, right: Any) -> Any

Compute the multiply of the inputs.

Parameters:

Name Type Description Default
left Any

The left encrypted operand.

 required
right Any

The right encrypted operand.

 required

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def multiply(left: Any, right: Any) -> Any:
    """Compute the multiply of the inputs.

        Args:
            left (Any): The left encrypted operand.
            right (Any): The right encrypted operand.

        Returns:
            Any: The result of the operation.
        """
    return left * right

negate 

negate(value: Any) -> Any

Compute the negate of the inputs.

Parameters:

Name Type Description Default
value Any

The encrypted operand.

 required

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def negate(value: Any) -> Any:
    """Compute the negate of the inputs.

        Args:
            value (Any): The encrypted operand.

        Returns:
            Any: The result of the operation.
        """
    return -value

square 

square(value: Any) -> Any

Compute the square of the inputs.

Parameters:

Name Type Description Default
value Any

The encrypted operand.

 required

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def square(value: Any) -> Any:
    """Compute the square of the inputs.

        Args:
            value (Any): The encrypted operand.

        Returns:
            Any: The result of the operation.
        """
    return value * value

cube 

cube(value: Any) -> Any

Compute the cube of the inputs.

Parameters:

Name Type Description Default
value Any

The encrypted operand.

 required

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def cube(value: Any) -> Any:
    """Compute the cube of the inputs.

        Args:
            value (Any): The encrypted operand.

        Returns:
            Any: The result of the operation.
        """
    return value * value * value

equal 

equal(left: Any, right: Any) -> Any

Compute the equal of the inputs.

Parameters:

Name Type Description Default
left Any

The left encrypted operand.

 required
right Any

The right encrypted operand.

 required

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def equal(left: Any, right: Any) -> Any:
    """Compute the equal of the inputs.

        Args:
            left (Any): The left encrypted operand.
            right (Any): The right encrypted operand.

        Returns:
            Any: The result of the operation.
        """
    return (left == right) * 1

not_equal 

not_equal(left: Any, right: Any) -> Any

Compute the not equal of the inputs.

Parameters:

Name Type Description Default
left Any

The left encrypted operand.

 required
right Any

The right encrypted operand.

 required

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def not_equal(left: Any, right: Any) -> Any:
    """Compute the not equal of the inputs.

        Args:
            left (Any): The left encrypted operand.
            right (Any): The right encrypted operand.

        Returns:
            Any: The result of the operation.
        """
    return (left != right) * 1

less 

less(left: Any, right: Any) -> Any

Compute the less of the inputs.

Parameters:

Name Type Description Default
left Any

The left encrypted operand.

 required
right Any

The right encrypted operand.

 required

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def less(left: Any, right: Any) -> Any:
    """Compute the less of the inputs.

        Args:
            left (Any): The left encrypted operand.
            right (Any): The right encrypted operand.

        Returns:
            Any: The result of the operation.
        """
    return (left < right) * 1

less_equal 

less_equal(left: Any, right: Any) -> Any

Compute the less equal of the inputs.

Parameters:

Name Type Description Default
left Any

The left encrypted operand.

 required
right Any

The right encrypted operand.

 required

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def less_equal(left: Any, right: Any) -> Any:
    """Compute the less equal of the inputs.

        Args:
            left (Any): The left encrypted operand.
            right (Any): The right encrypted operand.

        Returns:
            Any: The result of the operation.
        """
    return (left <= right) * 1

greater 

greater(left: Any, right: Any) -> Any

Compute the greater of the inputs.

Parameters:

Name Type Description Default
left Any

The left encrypted operand.

 required
right Any

The right encrypted operand.

 required

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def greater(left: Any, right: Any) -> Any:
    """Compute the greater of the inputs.

        Args:
            left (Any): The left encrypted operand.
            right (Any): The right encrypted operand.

        Returns:
            Any: The result of the operation.
        """
    return (left > right) * 1

greater_equal 

greater_equal(left: Any, right: Any) -> Any

Compute the greater equal of the inputs.

Parameters:

Name Type Description Default
left Any

The left encrypted operand.

 required
right Any

The right encrypted operand.

 required

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def greater_equal(left: Any, right: Any) -> Any:
    """Compute the greater equal of the inputs.

        Args:
            left (Any): The left encrypted operand.
            right (Any): The right encrypted operand.

        Returns:
            Any: The result of the operation.
        """
    return (left >= right) * 1

is_zero 

is_zero(value: Any) -> Any

Compute the is zero of the inputs.

Parameters:

Name Type Description Default
value Any

The encrypted operand.

 required

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def is_zero(value: Any) -> Any:
    """Compute the is zero of the inputs.

        Args:
            value (Any): The encrypted operand.

        Returns:
            Any: The result of the operation.
        """
    return (value == 0) * 1

maximum 

maximum(left: Any, right: Any) -> Any

Compute the maximum of the inputs.

Parameters:

Name Type Description Default
left Any

The left encrypted operand.

 required
right Any

The right encrypted operand.

 required

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def maximum(left: Any, right: Any) -> Any:
    """Compute the maximum of the inputs.

        Args:
            left (Any): The left encrypted operand.
            right (Any): The right encrypted operand.

        Returns:
            Any: The result of the operation.
        """
    return ((left+right)+abs(left-right))//2

minimum 

minimum(left: Any, right: Any) -> Any

Compute the minimum of the inputs.

Parameters:

Name Type Description Default
left Any

The left encrypted operand.

 required
right Any

The right encrypted operand.

 required

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def minimum(left: Any, right: Any) -> Any:
    """Compute the minimum of the inputs.

        Args:
            left (Any): The left encrypted operand.
            right (Any): The right encrypted operand.

        Returns:
            Any: The result of the operation.
        """
    return ((left+right)-abs(left-right))//2

make_scalar_multiply 

make_scalar_multiply(multiplier: int) -> UnaryFunction

Create a scalar multiply function.

Parameters:

Name Type Description Default
multiplier int

The cleartext multiplier.

 required

Returns:

Name Type Description
UnaryFunction UnaryFunction

The generated function.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def make_scalar_multiply(multiplier: int) -> UnaryFunction:
    """Create a scalar multiply function.

        Args:
            multiplier (int): The cleartext multiplier.

        Returns:
            UnaryFunction: The generated function.
        """
    normalized = validate_integer("multiplier", multiplier)

    def scalar_multiply(value: Any) -> Any:
        """Compute the scalar_multiply operation."""
        return value * normalized

    return scalar_multiply

make_is_close 

make_is_close(absolute_tolerance: int) -> BinaryFunction

Create a is close function.

Parameters:

Name Type Description Default
absolute_tolerance int

The absolute_tolerance.

 required

Returns:

Name Type Description
BinaryFunction BinaryFunction

The generated function.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def make_is_close(absolute_tolerance: int) -> BinaryFunction:
    """Create a is close function.

        Args:
            absolute_tolerance (int): The absolute_tolerance.

        Returns:
            BinaryFunction: The generated function.
        """
    tolerance = validate_integer(
        "absolute_tolerance",
        absolute_tolerance,
        minimum=0,
    )

    def is_close(left: Any, right: Any) -> Any:
        """Compute the is_close operation."""
        difference = left - right
        return (difference >= -tolerance) * (difference <= tolerance)

    return is_close

compile_add 

compile_add(min_left: int = 0, max_left: int = 15, min_right: int = 0, max_right: int = 15, *, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for add.

Parameters:

Name Type Description Default
min_left int

The lower bound for the left encrypted operand.

 0
max_left int

The upper bound for the left encrypted operand.

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min_right int

The lower bound for the right encrypted operand.

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max_right int

The upper bound for the right encrypted operand.

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configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_add(
    min_left: int = 0,
    max_left: int = 15,
    min_right: int = 0,
    max_right: int = 15,
    *,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for add.

        Args:
            min_left (int): The lower bound for the left encrypted operand.
            max_left (int): The upper bound for the left encrypted operand.
            min_right (int): The lower bound for the right encrypted operand.
            max_right (int): The upper bound for the right encrypted operand.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    return _compile_binary_native(
        add,
        min_left,
        max_left,
        min_right,
        max_right,
        configuration,
    )

compile_subtract 

compile_subtract(min_left: int = 0, max_left: int = 15, min_right: int = 0, max_right: int = 15, *, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for subtract.

Parameters:

Name Type Description Default
min_left int

The lower bound for the left encrypted operand.

 0
max_left int

The upper bound for the left encrypted operand.

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min_right int

The lower bound for the right encrypted operand.

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max_right int

The upper bound for the right encrypted operand.

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configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_subtract(
    min_left: int = 0,
    max_left: int = 15,
    min_right: int = 0,
    max_right: int = 15,
    *,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for subtract.

        Args:
            min_left (int): The lower bound for the left encrypted operand.
            max_left (int): The upper bound for the left encrypted operand.
            min_right (int): The lower bound for the right encrypted operand.
            max_right (int): The upper bound for the right encrypted operand.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    return _compile_binary_native(
        subtract,
        min_left,
        max_left,
        min_right,
        max_right,
        configuration,
    )

compile_multiply 

compile_multiply(min_left: int = 0, max_left: int = 15, min_right: int = 0, max_right: int = 15, *, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for multiply.

Parameters:

Name Type Description Default
min_left int

The lower bound for the left encrypted operand.

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max_left int

The upper bound for the left encrypted operand.

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min_right int

The lower bound for the right encrypted operand.

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max_right int

The upper bound for the right encrypted operand.

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configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_multiply(
    min_left: int = 0,
    max_left: int = 15,
    min_right: int = 0,
    max_right: int = 15,
    *,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for multiply.

        Args:
            min_left (int): The lower bound for the left encrypted operand.
            max_left (int): The upper bound for the left encrypted operand.
            min_right (int): The lower bound for the right encrypted operand.
            max_right (int): The upper bound for the right encrypted operand.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    return _compile_binary_native(
        multiply,
        min_left,
        max_left,
        min_right,
        max_right,
        configuration,
    )

compile_negate 

compile_negate(min_value: int = -15, max_value: int = 15, *, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for negate.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_negate(
    min_value: int = -15,
    max_value: int = 15,
    *,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for negate.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    minimum, maximum = validate_bounds(min_value, max_value)
    return compile_function(
        negate,
        {"value": "encrypted"},
        [minimum, maximum],
        configuration,
    )

compile_square 

compile_square(min_value: int = -15, max_value: int = 15, *, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for square.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_square(
    min_value: int = -15,
    max_value: int = 15,
    *,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for square.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    minimum, maximum = validate_bounds(min_value, max_value)
    inputset = [minimum, maximum]
    if minimum <= 0 <= maximum:
        inputset.append(0)
    return compile_function(
        square,
        {"value": "encrypted"},
        inputset,
        configuration,
    )

compile_cube 

compile_cube(min_value: int = -15, max_value: int = 15, *, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for cube.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_cube(
    min_value: int = -15,
    max_value: int = 15,
    *,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for cube.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    minimum, maximum = validate_bounds(min_value, max_value)
    inputset = [minimum, maximum]
    if minimum <= 0 <= maximum:
        inputset.append(0)
    return compile_function(
        cube,
        {"value": "encrypted"},
        inputset,
        configuration,
    )

compile_scalar_multiply 

compile_scalar_multiply(min_value: int, max_value: int, multiplier: int, *, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for scalar multiply.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 required
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 required
multiplier int

The cleartext multiplier.

 required
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_scalar_multiply(
    min_value: int,
    max_value: int,
    multiplier: int,
    *,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for scalar multiply.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            multiplier (int): The cleartext multiplier.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    minimum, maximum = validate_bounds(min_value, max_value)
    function = make_scalar_multiply(multiplier)
    return compile_function(
        function,
        {"value": "encrypted"},
        [minimum, maximum],
        configuration,
    )

compile_equal 

compile_equal(min_value: int = -15, max_value: int = 15, *, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for equal.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_equal(
    min_value: int = -15,
    max_value: int = 15,
    *,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for equal.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    return _compile_predicate(equal, min_value, max_value, configuration)

compile_not_equal 

compile_not_equal(min_value: int = -15, max_value: int = 15, *, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for not equal.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_not_equal(
    min_value: int = -15,
    max_value: int = 15,
    *,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for not equal.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    return _compile_predicate(not_equal, min_value, max_value, configuration)

compile_less 

compile_less(min_value: int = -15, max_value: int = 15, *, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for less.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_less(
    min_value: int = -15,
    max_value: int = 15,
    *,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for less.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    return _compile_predicate(less, min_value, max_value, configuration)

compile_less_equal 

compile_less_equal(min_value: int = -15, max_value: int = 15, *, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for less equal.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_less_equal(
    min_value: int = -15,
    max_value: int = 15,
    *,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for less equal.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    return _compile_predicate(less_equal, min_value, max_value, configuration)

compile_greater 

compile_greater(min_value: int = -15, max_value: int = 15, *, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for greater.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_greater(
    min_value: int = -15,
    max_value: int = 15,
    *,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for greater.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    return _compile_predicate(greater, min_value, max_value, configuration)

compile_greater_equal 

compile_greater_equal(min_value: int = -15, max_value: int = 15, *, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for greater equal.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_greater_equal(
    min_value: int = -15,
    max_value: int = 15,
    *,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for greater equal.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    return _compile_predicate(greater_equal, min_value, max_value, configuration)

compile_is_zero 

compile_is_zero(min_value: int = -15, max_value: int = 15, *, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for is zero.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_is_zero(
    min_value: int = -15,
    max_value: int = 15,
    *,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for is zero.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    minimum, maximum = validate_bounds(min_value, max_value)
    return compile_function(
        is_zero,
        {"value": "encrypted"},
        [minimum, 0, maximum],
        configuration,
    )

compile_maximum 

compile_maximum(min_left: int = 0, max_left: int = 15, min_right: int = 0, max_right: int = 15, *, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for maximum.

Parameters:

Name Type Description Default
min_left int

The lower bound for the left encrypted operand.

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max_left int

The upper bound for the left encrypted operand.

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min_right int

The lower bound for the right encrypted operand.

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max_right int

The upper bound for the right encrypted operand.

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configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_maximum(
    min_left: int = 0,
    max_left: int = 15,
    min_right: int = 0,
    max_right: int = 15,
    *,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for maximum.

        Args:
            min_left (int): The lower bound for the left encrypted operand.
            max_left (int): The upper bound for the left encrypted operand.
            min_right (int): The lower bound for the right encrypted operand.
            max_right (int): The upper bound for the right encrypted operand.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    return _compile_binary_native(
        maximum,
        min_left,
        max_left,
        min_right,
        max_right,
        configuration,
    )

compile_minimum 

compile_minimum(min_left: int = 0, max_left: int = 15, min_right: int = 0, max_right: int = 15, *, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for minimum.

Parameters:

Name Type Description Default
min_left int

The lower bound for the left encrypted operand.

 0
max_left int

The upper bound for the left encrypted operand.

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min_right int

The lower bound for the right encrypted operand.

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max_right int

The upper bound for the right encrypted operand.

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configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_minimum(
    min_left: int = 0,
    max_left: int = 15,
    min_right: int = 0,
    max_right: int = 15,
    *,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for minimum.

        Args:
            min_left (int): The lower bound for the left encrypted operand.
            max_left (int): The upper bound for the left encrypted operand.
            min_right (int): The lower bound for the right encrypted operand.
            max_right (int): The upper bound for the right encrypted operand.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    return _compile_binary_native(
        minimum,
        min_left,
        max_left,
        min_right,
        max_right,
        configuration,
    )

compile_is_close 

compile_is_close(min_value: int, max_value: int, *, absolute_tolerance: int, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for is close.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 required
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 required
absolute_tolerance int

The absolute_tolerance.

 required
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_is_close(
    min_value: int,
    max_value: int,
    *,
    absolute_tolerance: int,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for is close.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            absolute_tolerance (int): The absolute_tolerance.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    function = make_is_close(absolute_tolerance)
    return _compile_predicate(function, min_value, max_value, configuration)

make_absolute 

make_absolute(min_value: int, max_value: int) -> UnaryFunction

Create a absolute function.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 required
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 required

Returns:

Name Type Description
UnaryFunction UnaryFunction

The generated function.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def make_absolute(min_value: int, max_value: int) -> UnaryFunction:
    """Create a absolute function.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.

        Returns:
            UnaryFunction: The generated function.
        """
    values = unary_values(abs, min_value, max_value)
    return make_unary_lookup(values, min_value)

compile_absolute 

compile_absolute(min_value: int, max_value: int, *, allow_large_lookup: bool = False, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for absolute.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 required
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 required
allow_large_lookup bool

Whether to allow large table lookups (may be slow).

 False
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_absolute(
    min_value: int,
    max_value: int,
    *,
    allow_large_lookup: bool = False,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for absolute.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            allow_large_lookup (bool): Whether to allow large table lookups (may be slow).
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    check_lookup_domain(
        "compile_absolute",
        (min_value, max_value),
        allow_large_lookup=allow_large_lookup,
    )
    values = unary_values(abs, min_value, max_value)
    return compile_unary_lookup(
        "compile_absolute",
        values,
        min_value,
        max_value,
        allow_large_lookup=allow_large_lookup,
        configuration=configuration,
    )

make_clamp 

make_clamp(min_input: int, max_input: int, min_value: int, max_value: int) -> UnaryFunction

Create a clamp function.

Parameters:

Name Type Description Default
min_input int

The min_input.

 required
max_input int

The max_input.

 required
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 required
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 required

Returns:

Name Type Description
UnaryFunction UnaryFunction

The generated function.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def make_clamp(
    min_input: int,
    max_input: int,
    min_value: int,
    max_value: int,
) -> UnaryFunction:
    """Create a clamp function.

        Args:
            min_input (int): The min_input.
            max_input (int): The max_input.
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.

        Returns:
            UnaryFunction: The generated function.
        """
    input_minimum, input_maximum = validate_bounds(min_input, max_input)
    clamp_minimum, clamp_maximum = validate_bounds(min_value, max_value)
    values = unary_values(
        lambda value: max(clamp_minimum, min(value, clamp_maximum)),
        input_minimum,
        input_maximum,
    )
    return make_unary_lookup(values, input_minimum)

compile_clamp 

compile_clamp(min_input: int, max_input: int, min_value: int, max_value: int, *, allow_large_lookup: bool = False, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for clamp.

Parameters:

Name Type Description Default
min_input int

The min_input.

 required
max_input int

The max_input.

 required
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 required
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 required
allow_large_lookup bool

Whether to allow large table lookups (may be slow).

 False
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_clamp(
    min_input: int,
    max_input: int,
    min_value: int,
    max_value: int,
    *,
    allow_large_lookup: bool = False,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for clamp.

        Args:
            min_input (int): The min_input.
            max_input (int): The max_input.
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            allow_large_lookup (bool): Whether to allow large table lookups (may be slow).
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    check_lookup_domain(
        "compile_clamp",
        (min_input, max_input),
        allow_large_lookup=allow_large_lookup,
    )
    input_minimum, input_maximum = validate_bounds(min_input, max_input)
    clamp_minimum, clamp_maximum = validate_bounds(min_value, max_value)
    values = unary_values(
        lambda value: max(clamp_minimum, min(value, clamp_maximum)),
        input_minimum,
        input_maximum,
    )
    return compile_unary_lookup(
        "compile_clamp",
        values,
        input_minimum,
        input_maximum,
        allow_large_lookup=allow_large_lookup,
        configuration=configuration,
    )

make_modulo 

make_modulo(min_numerator: int, max_numerator: int, min_denominator: int, max_denominator: int, *, zero_result: int = 0) -> BinaryFunction

Create a modulo function.

Parameters:

Name Type Description Default
min_numerator int

The lower bound for the encrypted numerator.

 required
max_numerator int

The upper bound for the encrypted numerator.

 required
min_denominator int

The lower bound for the encrypted denominator.

 required
max_denominator int

The upper bound for the encrypted denominator.

 required
zero_result int

Result to return when the operation is undefined (e.g., division by zero).

 0

Returns:

Name Type Description
BinaryFunction BinaryFunction

The generated function.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def make_modulo(
    min_numerator: int,
    max_numerator: int,
    min_denominator: int,
    max_denominator: int,
    *,
    zero_result: int = 0,
) -> BinaryFunction:
    """Create a modulo function.

        Args:
            min_numerator (int): The lower bound for the encrypted numerator.
            max_numerator (int): The upper bound for the encrypted numerator.
            min_denominator (int): The lower bound for the encrypted denominator.
            max_denominator (int): The upper bound for the encrypted denominator.
            zero_result (int): Result to return when the operation is undefined (e.g., division by zero).

        Returns:
            BinaryFunction: The generated function.
        """
    zero = validate_integer("zero_result", zero_result)
    values = binary_values(
        lambda numerator, denominator: (
            zero if denominator == 0 else numerator % denominator
        ),
        min_numerator,
        max_numerator,
        min_denominator,
        max_denominator,
    )
    denominator_minimum, denominator_maximum = validate_bounds(
        min_denominator,
        max_denominator,
    )
    return make_binary_lookup(
        values,
        min_numerator,
        denominator_minimum,
        denominator_maximum - denominator_minimum + 1,
    )

compile_modulo 

compile_modulo(min_numerator: int, max_numerator: int, min_denominator: int, max_denominator: int, *, zero_result: int = 0, allow_large_lookup: bool = False, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for modulo.

Parameters:

Name Type Description Default
min_numerator int

The lower bound for the encrypted numerator.

 required
max_numerator int

The upper bound for the encrypted numerator.

 required
min_denominator int

The lower bound for the encrypted denominator.

 required
max_denominator int

The upper bound for the encrypted denominator.

 required
zero_result int

Result to return when the operation is undefined (e.g., division by zero).

 0
allow_large_lookup bool

Whether to allow large table lookups (may be slow).

 False
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_modulo(
    min_numerator: int,
    max_numerator: int,
    min_denominator: int,
    max_denominator: int,
    *,
    zero_result: int = 0,
    allow_large_lookup: bool = False,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for modulo.

        Args:
            min_numerator (int): The lower bound for the encrypted numerator.
            max_numerator (int): The upper bound for the encrypted numerator.
            min_denominator (int): The lower bound for the encrypted denominator.
            max_denominator (int): The upper bound for the encrypted denominator.
            zero_result (int): Result to return when the operation is undefined (e.g., division by zero).
            allow_large_lookup (bool): Whether to allow large table lookups (may be slow).
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    check_lookup_domain(
        "compile_modulo",
        (min_numerator, max_numerator),
        (min_denominator, max_denominator),
        allow_large_lookup=allow_large_lookup,
    )
    zero = validate_integer("zero_result", zero_result)
    values = binary_values(
        lambda numerator, denominator: (
            zero if denominator == 0 else numerator % denominator
        ),
        min_numerator,
        max_numerator,
        min_denominator,
        max_denominator,
    )
    return compile_binary_lookup(
        "compile_modulo",
        values,
        min_numerator,
        max_numerator,
        min_denominator,
        max_denominator,
        allow_large_lookup=allow_large_lookup,
        configuration=configuration,
    )

make_divmod 

make_divmod(min_numerator: int, max_numerator: int, min_denominator: int, max_denominator: int, *, zero_quotient: int = 0, zero_remainder: int = 0) -> BinaryFunction

Create a divmod function.

Parameters:

Name Type Description Default
min_numerator int

The lower bound for the encrypted numerator.

 required
max_numerator int

The upper bound for the encrypted numerator.

 required
min_denominator int

The lower bound for the encrypted denominator.

 required
max_denominator int

The upper bound for the encrypted denominator.

 required
zero_quotient int

Result to return for quotient when division by zero.

 0
zero_remainder int

Result to return for remainder when division by zero.

 0

Returns:

Name Type Description
BinaryFunction BinaryFunction

The generated function.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def make_divmod(
    min_numerator: int,
    max_numerator: int,
    min_denominator: int,
    max_denominator: int,
    *,
    zero_quotient: int = 0,
    zero_remainder: int = 0,
) -> BinaryFunction:
    """Create a divmod function.

        Args:
            min_numerator (int): The lower bound for the encrypted numerator.
            max_numerator (int): The upper bound for the encrypted numerator.
            min_denominator (int): The lower bound for the encrypted denominator.
            max_denominator (int): The upper bound for the encrypted denominator.
            zero_quotient (int): Result to return for quotient when division by zero.
            zero_remainder (int): Result to return for remainder when division by zero.

        Returns:
            BinaryFunction: The generated function.
        """
    zero_q = validate_integer("zero_quotient", zero_quotient)
    zero_r = validate_integer("zero_remainder", zero_remainder)
    denominator_minimum, denominator_maximum = validate_bounds(
        min_denominator,
        max_denominator,
    )
    quotient_values = binary_values(
        lambda numerator, denominator: (
            zero_q if denominator == 0 else numerator // denominator
        ),
        min_numerator,
        max_numerator,
        denominator_minimum,
        denominator_maximum,
    )
    remainder_values = binary_values(
        lambda numerator, denominator: (
            zero_r if denominator == 0 else numerator % denominator
        ),
        min_numerator,
        max_numerator,
        denominator_minimum,
        denominator_maximum,
    )
    width = denominator_maximum - denominator_minimum + 1
    quotient = make_binary_lookup(
        quotient_values,
        min_numerator,
        denominator_minimum,
        width,
    )
    remainder = make_binary_lookup(
        remainder_values,
        min_numerator,
        denominator_minimum,
        width,
    )

    def quotient_and_remainder(numerator: Any, denominator: Any) -> Any:
        """Compute the quotient and remainder operations."""
        return quotient(numerator, denominator), remainder(numerator, denominator)

    return quotient_and_remainder

compile_divmod 

compile_divmod(min_numerator: int, max_numerator: int, min_denominator: int, max_denominator: int, *, zero_quotient: int = 0, zero_remainder: int = 0, allow_large_lookup: bool = False, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for divmod.

Parameters:

Name Type Description Default
min_numerator int

The lower bound for the encrypted numerator.

 required
max_numerator int

The upper bound for the encrypted numerator.

 required
min_denominator int

The lower bound for the encrypted denominator.

 required
max_denominator int

The upper bound for the encrypted denominator.

 required
zero_quotient int

Result to return for quotient when division by zero.

 0
zero_remainder int

Result to return for remainder when division by zero.

 0
allow_large_lookup bool

Whether to allow large table lookups (may be slow).

 False
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_divmod(
    min_numerator: int,
    max_numerator: int,
    min_denominator: int,
    max_denominator: int,
    *,
    zero_quotient: int = 0,
    zero_remainder: int = 0,
    allow_large_lookup: bool = False,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for divmod.

        Args:
            min_numerator (int): The lower bound for the encrypted numerator.
            max_numerator (int): The upper bound for the encrypted numerator.
            min_denominator (int): The lower bound for the encrypted denominator.
            max_denominator (int): The upper bound for the encrypted denominator.
            zero_quotient (int): Result to return for quotient when division by zero.
            zero_remainder (int): Result to return for remainder when division by zero.
            allow_large_lookup (bool): Whether to allow large table lookups (may be slow).
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    check_lookup_domain(
        "compile_divmod",
        (min_numerator, max_numerator),
        (min_denominator, max_denominator),
        allow_large_lookup=allow_large_lookup,
    )
    function = make_divmod(
        min_numerator,
        max_numerator,
        min_denominator,
        max_denominator,
        zero_quotient=zero_quotient,
        zero_remainder=zero_remainder,
    )
    numerator_minimum, numerator_maximum = validate_bounds(
        min_numerator,
        max_numerator,
    )
    denominator_minimum, denominator_maximum = validate_bounds(
        min_denominator,
        max_denominator,
    )
    quotient_values = binary_values(
        lambda numerator, denominator: (
            zero_quotient if denominator == 0 else numerator // denominator
        ),
        numerator_minimum,
        numerator_maximum,
        denominator_minimum,
        denominator_maximum,
    )
    remainder_values = binary_values(
        lambda numerator, denominator: (
            zero_remainder if denominator == 0 else numerator % denominator
        ),
        numerator_minimum,
        numerator_maximum,
        denominator_minimum,
        denominator_maximum,
    )
    check_lookup_cost(
        "compile_divmod quotient",
        quotient_values,
        allow_large_lookup=allow_large_lookup,
    )
    check_lookup_cost(
        "compile_divmod remainder",
        remainder_values,
        allow_large_lookup=allow_large_lookup,
    )
    inputset = _binary_inputset(
        numerator_minimum,
        numerator_maximum,
        denominator_minimum,
        denominator_maximum,
    )

    if denominator_minimum <= 0 <= denominator_maximum:
        inputset.append((numerator_minimum, 0))
        inputset.append((numerator_maximum, 0))

    return compile_function(
        function,
        {"numerator": "encrypted", "denominator": "encrypted"},
        inputset,
        configuration,
    )

select 

select(control: Any, when_true: Any, when_false: Any) -> Any

Compute the select of the inputs.

Parameters:

Name Type Description Default
control Any

The control.

 required
when_true Any

The when_true.

 required
when_false Any

The when_false.

 required

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def select(control: Any, when_true: Any, when_false: Any) -> Any:
    """Compute the select of the inputs.

        Args:
            control (Any): The control.
            when_true (Any): The when_true.
            when_false (Any): The when_false.

        Returns:
            Any: The result of the operation.
        """
    return control * (when_true - when_false) + when_false

compile_select 

compile_select(min_value: int = -15, max_value: int = 15, *, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for select.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_select(
    min_value: int = -15,
    max_value: int = 15,
    *,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for select.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    minimum, maximum = validate_bounds(min_value, max_value)
    inputset = [
        (0, minimum, minimum),
        (0, maximum, maximum),
        (0, minimum, maximum),
        (1, minimum, minimum),
        (1, maximum, maximum),
        (1, maximum, minimum),
    ]
    return compile_function(
        select,
        {
            "control": "encrypted",
            "when_true": "encrypted",
            "when_false": "encrypted",
        },
        inputset,
        configuration,
    )

make_abs_diff 

make_abs_diff(min_value: int = 0, max_value: int = 15) -> BinaryFunction

Create a abs diff function.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 0
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15

Returns:

Name Type Description
BinaryFunction BinaryFunction

The generated function.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def make_abs_diff(min_value: int = 0, max_value: int = 15) -> BinaryFunction:
    """Create a abs diff function.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.

        Returns:
            BinaryFunction: The generated function.
        """
    minimum, maximum = validate_bounds(min_value, max_value)
    span = maximum - minimum

    if span == 0:
        def constant_abs_diff(left: Any, right: Any) -> Any:
            """Compute the constant_abs_diff operation."""
            return left - right

        return constant_abs_diff

    values = unary_values(abs, -span, span)
    lookup = make_unary_lookup(values, -span)

    def abs_diff(left: Any, right: Any) -> Any:
        """Compute the abs_diff operation."""
        return lookup(left - right)

    return abs_diff

compile_abs_diff 

compile_abs_diff(min_value: int = 0, max_value: int = 15, *, allow_large_lookup: bool = False, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for abs diff.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 0
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15
allow_large_lookup bool

Whether to allow large table lookups (may be slow).

 False
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_abs_diff(
    min_value: int = 0,
    max_value: int = 15,
    *,
    allow_large_lookup: bool = False,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for abs diff.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            allow_large_lookup (bool): Whether to allow large table lookups (may be slow).
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    low, high = validate_bounds(min_value, max_value)
    check_lookup_domain(
        "compile_abs_diff",
        (-(high - low), high - low),
        allow_large_lookup=allow_large_lookup,
    )
    minimum, maximum = validate_bounds(min_value, max_value)
    span = maximum - minimum
    if span:
        check_lookup_cost(
            "compile_abs_diff",
            unary_values(abs, -span, span),
            allow_large_lookup=allow_large_lookup,
        )
    function = make_abs_diff(minimum, maximum)
    inputset = [
        (minimum, minimum),
        (minimum, maximum),
        (maximum, minimum),
        (maximum, maximum),
    ]
    return compile_function(
        function,
        {"left": "encrypted", "right": "encrypted"},
        inputset,
        configuration,
    )

make_copysign 

make_copysign(min_value: int = -15, max_value: int = 15) -> BinaryFunction

Create a copysign function.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15

Returns:

Name Type Description
BinaryFunction BinaryFunction

The generated function.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def make_copysign(min_value: int = -15, max_value: int = 15) -> BinaryFunction:
    """Create a copysign function.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.

        Returns:
            BinaryFunction: The generated function.
        """
    minimum, maximum = validate_bounds(min_value, max_value)
    absolute = make_absolute(minimum, maximum)

    def copysign(x: Any, y: Any) -> Any:
        """Compute the copysign operation."""
        sign_factor = (y >= 0) * 2 - 1
        return absolute(x) * sign_factor

    return copysign

compile_copysign 

compile_copysign(min_value: int = -15, max_value: int = 15, *, allow_large_lookup: bool = False, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for copysign.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15
allow_large_lookup bool

Whether to allow large table lookups (may be slow).

 False
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_copysign(
    min_value: int = -15,
    max_value: int = 15,
    *,
    allow_large_lookup: bool = False,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for copysign.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            allow_large_lookup (bool): Whether to allow large table lookups (may be slow).
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    check_lookup_domain(
        "compile_copysign",
        (min_value, max_value),
        allow_large_lookup=allow_large_lookup,
    )
    minimum, maximum = validate_bounds(min_value, max_value)
    check_lookup_cost(
        "compile_copysign",
        unary_values(abs, minimum, maximum),
        allow_large_lookup=allow_large_lookup,
    )
    function = make_copysign(minimum, maximum)
    inputset = [
        (minimum, minimum),
        (minimum, maximum),
        (maximum, minimum),
        (maximum, maximum),
    ]
    return compile_function(
        function,
        {"x": "encrypted", "y": "encrypted"},
        inputset,
        configuration,
    )

make_saturating_add 

make_saturating_add(min_value: int = -15, max_value: int = 15) -> BinaryFunction

Create a saturating add function.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15

Returns:

Name Type Description
BinaryFunction BinaryFunction

The generated function.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def make_saturating_add(min_value: int = -15, max_value: int = 15) -> BinaryFunction:
    """Create a saturating add function.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.

        Returns:
            BinaryFunction: The generated function.
        """
    return _make_saturating("add", min_value, max_value)

make_saturating_subtract 

make_saturating_subtract(min_value: int = -15, max_value: int = 15) -> BinaryFunction

Create a saturating subtract function.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15

Returns:

Name Type Description
BinaryFunction BinaryFunction

The generated function.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def make_saturating_subtract(min_value: int = -15, max_value: int = 15) -> BinaryFunction:
    """Create a saturating subtract function.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.

        Returns:
            BinaryFunction: The generated function.
        """
    return _make_saturating("subtract", min_value, max_value)

make_saturating_multiply 

make_saturating_multiply(min_value: int = -15, max_value: int = 15) -> BinaryFunction

Create a saturating multiply function.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15

Returns:

Name Type Description
BinaryFunction BinaryFunction

The generated function.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def make_saturating_multiply(min_value: int = -15, max_value: int = 15) -> BinaryFunction:
    """Create a saturating multiply function.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.

        Returns:
            BinaryFunction: The generated function.
        """
    return _make_saturating("multiply", min_value, max_value)

compile_saturating_add 

compile_saturating_add(min_value: int = -15, max_value: int = 15, *, allow_large_lookup: bool = False, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for saturating add.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15
allow_large_lookup bool

Whether to allow large table lookups (may be slow).

 False
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_saturating_add(
    min_value: int = -15,
    max_value: int = 15,
    *,
    allow_large_lookup: bool = False,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for saturating add.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            allow_large_lookup (bool): Whether to allow large table lookups (may be slow).
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    return _compile_saturating("add", min_value, max_value, allow_large_lookup, configuration)

compile_saturating_subtract 

compile_saturating_subtract(min_value: int = -15, max_value: int = 15, *, allow_large_lookup: bool = False, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for saturating subtract.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15
allow_large_lookup bool

Whether to allow large table lookups (may be slow).

 False
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_saturating_subtract(
    min_value: int = -15,
    max_value: int = 15,
    *,
    allow_large_lookup: bool = False,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for saturating subtract.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            allow_large_lookup (bool): Whether to allow large table lookups (may be slow).
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    return _compile_saturating(
        "subtract", min_value, max_value, allow_large_lookup, configuration
    )

compile_saturating_multiply 

compile_saturating_multiply(min_value: int = -15, max_value: int = 15, *, allow_large_lookup: bool = False, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for saturating multiply.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15
allow_large_lookup bool

Whether to allow large table lookups (may be slow).

 False
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_saturating_multiply(
    min_value: int = -15,
    max_value: int = 15,
    *,
    allow_large_lookup: bool = False,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for saturating multiply.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            allow_large_lookup (bool): Whether to allow large table lookups (may be slow).
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    return _compile_saturating(
        "multiply", min_value, max_value, allow_large_lookup, configuration
    )

make_fdim 

make_fdim(min_value: int = 0, max_value: int = 15) -> BinaryFunction

Create a fdim function.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 0
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15

Returns:

Name Type Description
BinaryFunction BinaryFunction

The generated function.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def make_fdim(min_value: int = 0, max_value: int = 15) -> BinaryFunction:
    """Create a fdim function.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.

        Returns:
            BinaryFunction: The generated function.
        """
    minimum, maximum = validate_bounds(min_value, max_value)
    span = maximum - minimum

    if span == 0:
        def constant_fdim(left: Any, right: Any) -> Any:
            """Compute the constant_fdim operation."""
            return left - right

        return constant_fdim

    values = unary_values(lambda diff: max(diff, 0), -span, span)
    lookup = make_unary_lookup(values, -span)

    def fdim(left: Any, right: Any) -> Any:
        """Compute the fdim operation."""
        return lookup(left - right)

    return fdim

compile_fdim 

compile_fdim(min_value: int = 0, max_value: int = 15, *, allow_large_lookup: bool = False, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for fdim.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 0
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

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allow_large_lookup bool

Whether to allow large table lookups (may be slow).

 False
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_fdim(
    min_value: int = 0,
    max_value: int = 15,
    *,
    allow_large_lookup: bool = False,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for fdim.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            allow_large_lookup (bool): Whether to allow large table lookups (may be slow).
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    low, high = validate_bounds(min_value, max_value)
    check_lookup_domain(
        "compile_fdim",
        (0, 2 * (high - low)),
        allow_large_lookup=allow_large_lookup,
    )
    minimum, maximum = validate_bounds(min_value, max_value)
    span = maximum - minimum
    if span:
        check_lookup_cost(
            "compile_fdim",
            unary_values(lambda diff: max(diff, 0), -span, span),
            allow_large_lookup=allow_large_lookup,
        )
    function = make_fdim(minimum, maximum)
    inputset = [
        (minimum, minimum),
        (minimum, maximum),
        (maximum, minimum),
        (maximum, maximum),
    ]
    return compile_function(
        function,
        {"left": "encrypted", "right": "encrypted"},
        inputset,
        configuration,
    )

fma 

fma(left: Any, right: Any, addend: Any) -> Any

Compute the fma of the inputs.

Parameters:

Name Type Description Default
left Any

The left encrypted operand.

 required
right Any

The right encrypted operand.

 required
addend Any

The addend.

 required

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def fma(left: Any, right: Any, addend: Any) -> Any:
    """Compute the fma of the inputs.

        Args:
            left (Any): The left encrypted operand.
            right (Any): The right encrypted operand.
            addend (Any): The addend.

        Returns:
            Any: The result of the operation.
        """
    return left * right + addend

compile_fma 

compile_fma(min_value: int = -15, max_value: int = 15, *, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for fma.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 -15
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 15
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_fma(
    min_value: int = -15,
    max_value: int = 15,
    *,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for fma.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    minimum, maximum = validate_bounds(min_value, max_value)
    inputset = [
        (minimum, minimum, minimum),
        (minimum, maximum, minimum),
        (maximum, minimum, maximum),
        (maximum, maximum, maximum),
        (minimum, maximum, maximum),
        (maximum, maximum, minimum),
    ]
    return compile_function(
        fma,
        {"left": "encrypted", "right": "encrypted", "addend": "encrypted"},
        inputset,
        configuration,
    )

make_remainder 

make_remainder(min_numerator: int, max_numerator: int, min_denominator: int, max_denominator: int, *, zero_result: int = 0) -> BinaryFunction

Create a remainder function.

Parameters:

Name Type Description Default
min_numerator int

The lower bound for the encrypted numerator.

 required
max_numerator int

The upper bound for the encrypted numerator.

 required
min_denominator int

The lower bound for the encrypted denominator.

 required
max_denominator int

The upper bound for the encrypted denominator.

 required
zero_result int

Result to return when the operation is undefined (e.g., division by zero).

 0

Returns:

Name Type Description
BinaryFunction BinaryFunction

The generated function.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def make_remainder(
    min_numerator: int,
    max_numerator: int,
    min_denominator: int,
    max_denominator: int,
    *,
    zero_result: int = 0,
) -> BinaryFunction:
    """Create a remainder function.

        Args:
            min_numerator (int): The lower bound for the encrypted numerator.
            max_numerator (int): The upper bound for the encrypted numerator.
            min_denominator (int): The lower bound for the encrypted denominator.
            max_denominator (int): The upper bound for the encrypted denominator.
            zero_result (int): Result to return when the operation is undefined (e.g., division by zero).

        Returns:
            BinaryFunction: The generated function.
        """
    from fractions import Fraction

    zero = validate_integer("zero_result", zero_result)
    denominator_minimum, denominator_maximum = validate_bounds(
        min_denominator,
        max_denominator,
    )
    values = binary_values(
        lambda numerator, denominator: (
            zero
            if denominator == 0
            else numerator - round(Fraction(numerator, denominator)) * denominator
        ),
        min_numerator,
        max_numerator,
        denominator_minimum,
        denominator_maximum,
    )
    return make_binary_lookup(
        values,
        min_numerator,
        denominator_minimum,
        denominator_maximum - denominator_minimum + 1,
    )

compile_remainder 

compile_remainder(min_numerator: int, max_numerator: int, min_denominator: int, max_denominator: int, *, zero_result: int = 0, allow_large_lookup: bool = False, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for remainder.

Parameters:

Name Type Description Default
min_numerator int

The lower bound for the encrypted numerator.

 required
max_numerator int

The upper bound for the encrypted numerator.

 required
min_denominator int

The lower bound for the encrypted denominator.

 required
max_denominator int

The upper bound for the encrypted denominator.

 required
zero_result int

Result to return when the operation is undefined (e.g., division by zero).

 0
allow_large_lookup bool

Whether to allow large table lookups (may be slow).

 False
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_remainder(
    min_numerator: int,
    max_numerator: int,
    min_denominator: int,
    max_denominator: int,
    *,
    zero_result: int = 0,
    allow_large_lookup: bool = False,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for remainder.

        Args:
            min_numerator (int): The lower bound for the encrypted numerator.
            max_numerator (int): The upper bound for the encrypted numerator.
            min_denominator (int): The lower bound for the encrypted denominator.
            max_denominator (int): The upper bound for the encrypted denominator.
            zero_result (int): Result to return when the operation is undefined (e.g., division by zero).
            allow_large_lookup (bool): Whether to allow large table lookups (may be slow).
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    check_lookup_domain(
        "compile_remainder",
        (min_numerator, max_numerator),
        (min_denominator, max_denominator),
        allow_large_lookup=allow_large_lookup,
    )
    from fractions import Fraction

    zero = validate_integer("zero_result", zero_result)
    values = binary_values(
        lambda numerator, denominator: (
            zero
            if denominator == 0
            else numerator - round(Fraction(numerator, denominator)) * denominator
        ),
        min_numerator,
        max_numerator,
        min_denominator,
        max_denominator,
    )
    return compile_binary_lookup(
        "compile_remainder",
        values,
        min_numerator,
        max_numerator,
        min_denominator,
        max_denominator,
        allow_large_lookup=allow_large_lookup,
        configuration=configuration,
    )

make_ldexp 

make_ldexp(exponent: int) -> UnaryFunction

Create a ldexp function.

Parameters:

Name Type Description Default
exponent int

The exponent.

 required

Returns:

Name Type Description
UnaryFunction UnaryFunction

The generated function.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def make_ldexp(exponent: int) -> UnaryFunction:
    """Create a ldexp function.

        Args:
            exponent (int): The exponent.

        Returns:
            UnaryFunction: The generated function.
        """
    normalized = validate_integer("exponent", exponent)
    if normalized >= 0:
        factor = 1 << normalized

        def scale_up(value: Any) -> Any:
            """Compute the scale_up operation."""
            return value * factor

        return scale_up

    divisor = 1 << (-normalized)

    def scale_down(value: Any) -> Any:
        """Compute the scale_down operation."""
        return value // divisor

    return scale_down

compile_ldexp 

compile_ldexp(min_value: int, max_value: int, exponent: int, *, configuration: Optional[Configuration] = None) -> fhe.Circuit

Compile an FHE circuit for ldexp.

Parameters:

Name Type Description Default
min_value int

The lower bound for the encrypted inputs, used to dimension the FHE circuit.

 required
max_value int

The upper bound for the encrypted inputs, used to dimension the FHE circuit.

 required
exponent int

The exponent.

 required
configuration Optional[Configuration]

Optional FHE compiler configuration object.

 None

Returns:

Type Description
Circuit

fhe.Circuit: The compiled FHE circuit.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def compile_ldexp(
    min_value: int,
    max_value: int,
    exponent: int,
    *,
    configuration: Optional[fhe.Configuration] = None,
) -> fhe.Circuit:
    """Compile an FHE circuit for ldexp.

        Args:
            min_value (int): The lower bound for the encrypted inputs, used to dimension the FHE circuit.
            max_value (int): The upper bound for the encrypted inputs, used to dimension the FHE circuit.
            exponent (int): The exponent.
            configuration (Optional[fhe.Configuration]): Optional FHE compiler configuration object.

        Returns:
            fhe.Circuit: The compiled FHE circuit.
        """
    minimum, maximum = validate_bounds(min_value, max_value)
    function = make_ldexp(exponent)
    return compile_function(
        function,
        {"value": "encrypted"},
        [minimum, maximum],
        configuration,
    )

fsum 

fsum(values: Any) -> Any

Compute the fsum of the inputs.

Parameters:

Name Type Description Default
values Any

The values.

 required

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def fsum(values: Any) -> Any:
    """Compute the fsum of the inputs.

        Args:
            values (Any): The values.

        Returns:
            Any: The result of the operation.
        """
    items = list(values)
    if not items:
        return 0
    while len(items) > 1:
        next_items = []
        for index in range(0, len(items) - 1, 2):
            next_items.append(items[index] + items[index + 1])
        if len(items) % 2 == 1:
            next_items.append(items[-1])
        items = next_items
    return items[0]

prod 

prod(values: Any, start: int = 1) -> Any

Compute the prod of the inputs.

Parameters:

Name Type Description Default
values Any

The values.

 required
start int

The start.

 1

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def prod(values: Any, start: int = 1) -> Any:
    """Compute the prod of the inputs.

        Args:
            values (Any): The values.
            start (int): The start.

        Returns:
            Any: The result of the operation.
        """
    normalized_start = validate_integer("start", start)
    items = list(values)
    if not items:
        return normalized_start
    while len(items) > 1:
        next_items = []
        for index in range(0, len(items) - 1, 2):
            next_items.append(items[index] * items[index + 1])
        if len(items) % 2 == 1:
            next_items.append(items[-1])
        items = next_items
    return items[0] * normalized_start

sumprod 

sumprod(p: Any, q: Any) -> Any

Compute the sumprod of the inputs.

Parameters:

Name Type Description Default
p Any

The p.

 required
q Any

The q.

 required

Returns:

Name Type Description
Any Any

The result of the operation.
Source code in src/concrete_fhe_toolkit/math/basic.py 
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def sumprod(p: Any, q: Any) -> Any:
    """Compute the sumprod of the inputs.

        Args:
            p (Any): The p.
            q (Any): The q.

        Returns:
            Any: The result of the operation.
        """
    left = list(p)
    right = list(q)
    if len(left) != len(right):
        raise ValueError("p and q must have the same length")
    return fsum(item_p * item_q for item_p, item_q in zip(left, right))