"""
APE Extended Math Module (v1.0.0 Scaffold)

Advanced mathematical functions beyond basic arithmetic.

Author: David Van Aelst
Status: Scaffold - implementation pending
"""

from typing import Union

Number = Union[int, float]

# Mathematical constants
PI = 3.141592653589793
E = 2.718281828459045


# Trigonometric functions
def sin(x: Number) -> float:
    """
    Sine of x (x in radians).
    
    Example:
        result = math_ext.sin(PI / 2)  # 1.0
    
    TODO: Implement sine function
    """
    raise NotImplementedError("sin() not yet implemented")


def cos(x: Number) -> float:
    """
    Cosine of x (x in radians).
    
    Example:
        result = math_ext.cos(0)  # 1.0
    
    TODO: Implement cosine function
    """
    raise NotImplementedError("cos() not yet implemented")


def tan(x: Number) -> float:
    """
    Tangent of x (x in radians).
    
    Example:
        result = math_ext.tan(PI / 4)  # ~1.0
    
    TODO: Implement tangent function
    """
    raise NotImplementedError("tan() not yet implemented")


def asin(x: Number) -> float:
    """
    Arc sine of x (result in radians).
    
    Example:
        angle = math_ext.asin(0.5)  # PI / 6
    
    TODO: Implement arc sine function
    """
    raise NotImplementedError("asin() not yet implemented")


def acos(x: Number) -> float:
    """
    Arc cosine of x (result in radians).
    
    Example:
        angle = math_ext.acos(0.5)  # PI / 3
    
    TODO: Implement arc cosine function
    """
    raise NotImplementedError("acos() not yet implemented")


def atan(x: Number) -> float:
    """
    Arc tangent of x (result in radians).
    
    Example:
        angle = math_ext.atan(1)  # PI / 4
    
    TODO: Implement arc tangent function
    """
    raise NotImplementedError("atan() not yet implemented")


def atan2(y: Number, x: Number) -> float:
    """
    Arc tangent of y/x (result in radians), with correct quadrant.
    
    Example:
        angle = math_ext.atan2(1, 1)  # PI / 4
    
    TODO: Implement two-argument arc tangent
    """
    raise NotImplementedError("atan2() not yet implemented")


# Logarithmic functions
def log(x: Number, base: Number = E) -> float:
    """
    Logarithm of x to the given base (default natural log).
    
    Example:
        result = math_ext.log(E)  # 1.0 (natural log)
        result = math_ext.log(100, 10)  # 2.0 (log base 10)
    
    TODO: Implement logarithm function
    """
    raise NotImplementedError("log() not yet implemented")


def log10(x: Number) -> float:
    """
    Base-10 logarithm of x.
    
    Example:
        result = math_ext.log10(1000)  # 3.0
    
    TODO: Implement log10 function
    """
    raise NotImplementedError("log10() not yet implemented")


def ln(x: Number) -> float:
    """
    Natural logarithm of x (base e).
    
    Example:
        result = math_ext.ln(E)  # 1.0
    
    TODO: Implement natural log function
    """
    raise NotImplementedError("ln() not yet implemented")


# Rounding functions
def round(x: Number, decimals: int = 0) -> Number:
    """
    Round x to given number of decimal places.
    
    Example:
        result = math_ext.round(3.14159, 2)  # 3.14
    
    TODO: Implement rounding function
    """
    raise NotImplementedError("round() not yet implemented")


def floor(x: Number) -> int:
    """
    Largest integer less than or equal to x.
    
    Example:
        result = math_ext.floor(3.7)  # 3
        result = math_ext.floor(-2.3)  # -3
    
    TODO: Implement floor function
    """
    raise NotImplementedError("floor() not yet implemented")


def ceil(x: Number) -> int:
    """
    Smallest integer greater than or equal to x.
    
    Example:
        result = math_ext.ceil(3.2)  # 4
        result = math_ext.ceil(-2.7)  # -2
    
    TODO: Implement ceiling function
    """
    raise NotImplementedError("ceil() not yet implemented")


# Power and root functions
def sqrt(x: Number) -> float:
    """
    Square root of x.
    
    Example:
        result = math_ext.sqrt(16)  # 4.0
    
    TODO: Implement square root function
    """
    raise NotImplementedError("sqrt() not yet implemented")


def pow(x: Number, y: Number) -> float:
    """
    x raised to the power of y.
    
    Example:
        result = math_ext.pow(2, 8)  # 256.0
    
    TODO: Implement power function
    """
    raise NotImplementedError("pow() not yet implemented")


__all__ = [
    'PI', 'E',
    'sin', 'cos', 'tan', 'asin', 'acos', 'atan', 'atan2',
    'log', 'log10', 'ln',
    'round', 'floor', 'ceil',
    'sqrt', 'pow'
]
