# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
Miscellaneous utilities for `astropy.units`.

None of the functions in the module are meant for use outside of the
package.
"""

from fractions import Fraction
from typing import SupportsFloat

import numpy as np
from numpy import finfo

from .errors import UnitScaleError
from .typing import UnitPower, UnitPowerLike, UnitScale, UnitScaleLike

_float_finfo = finfo(float)
# take float here to ensure comparison with another float is fast
# give a little margin since often multiple calculations happened
_JUST_BELOW_UNITY = float(1.0 - 4.0 * _float_finfo.epsneg)
_JUST_ABOVE_UNITY = float(1.0 + 4.0 * _float_finfo.eps)


def is_effectively_unity(value: UnitScaleLike) -> bool | np.bool_:
    # value is *almost* always real, except, e.g., for u.mag**0.5, when
    # it will be complex.  Use try/except to ensure normal case is fast
    try:
        return _JUST_BELOW_UNITY <= value <= _JUST_ABOVE_UNITY
    except TypeError:  # value is complex
        return (
            _JUST_BELOW_UNITY <= value.real <= _JUST_ABOVE_UNITY
            and _JUST_BELOW_UNITY <= value.imag + 1 <= _JUST_ABOVE_UNITY
        )


def sanitize_scale(scale: UnitScaleLike) -> UnitScale:
    if is_effectively_unity(scale):
        return 1.0
    if not scale:
        raise UnitScaleError("cannot create a unit with a scale of 0.")
    if type(scale) is float:  # float is very common, so handle it fast
        return scale
    if isinstance(scale, SupportsFloat):
        return float(scale)

    if abs(scale.real) > abs(scale.imag):
        if is_effectively_unity(scale.imag / scale.real + 1):
            return float(scale.real)
    elif is_effectively_unity(scale.real / scale.imag + 1):
        return complex(0.0, scale.imag)
    return complex(scale)


def maybe_simple_fraction(p: UnitPowerLike, max_denominator: int = 100) -> UnitPower:
    """Fraction very close to x with denominator at most max_denominator.

    The fraction has to be such that fraction/x is unity to within 4 ulp.
    If such a fraction does not exist, returns the float number.

    The algorithm is that of `fractions.Fraction.limit_denominator`, but
    sped up by not creating a fraction to start with.

    If the input is zero, an integer or `fractions.Fraction`, just return it.
    """
    if p.__class__ is int or p.__class__ is Fraction:
        return p
    if p == 0:
        return 0  # p might be some numpy number, but we want a Python int
    n, d = float(p).as_integer_ratio()
    a = n // d
    # Normally, start with 0,1 and 1,0; here we have applied first iteration.
    n0, d0 = 1, 0
    n1, d1 = a, 1
    while d1 <= max_denominator:
        if _JUST_BELOW_UNITY <= n1 / (d1 * p) <= _JUST_ABOVE_UNITY:
            return Fraction(n1, d1)
        n, d = d, n - a * d
        a = n // d
        n0, n1 = n1, n0 + a * n1
        d0, d1 = d1, d0 + a * d1

    return float(p)


def sanitize_power(p: UnitPowerLike) -> UnitPower:
    """Convert the power to a float, an integer, or a Fraction.

    If a fractional power can be represented exactly as a floating point
    number, convert it to a float, to make the math much faster; otherwise,
    retain it as a `fractions.Fraction` object to avoid losing precision.
    Conversely, if the value is indistinguishable from a rational number with a
    low-numbered denominator, convert to a Fraction object.
    If a power can be represented as an integer, use that.

    Parameters
    ----------
    p : float, int, Rational, Fraction
        Power to be converted.
    """
    if p.__class__ is int:
        return p

    p = maybe_simple_fraction(p)
    if isinstance(p, float):
        return p  # If still a float, nothing more to be done.
    # Otherwise, check for simplifications.
    denom = p.denominator

    if denom == 1:
        return int(p.numerator)

    elif (denom & (denom - 1)) == 0:
        # Above is a bit-twiddling hack to see if denom is a power of two.
        # If so, float does not lose precision and will speed things up.
        p = float(p)

    return p


def resolve_fractions(
    a: UnitPowerLike, b: UnitPowerLike
) -> tuple[UnitPowerLike, UnitPowerLike]:
    """
    If either input is a Fraction, convert the other to a Fraction
    (at least if it does not have a ridiculous denominator).
    This ensures that any operation involving a Fraction will use
    rational arithmetic and preserve precision.
    """
    # We short-circuit on the most common cases of int and float, since
    # isinstance(a, Fraction) is very slow for any non-Fraction instances.
    a_is_fraction = (
        a.__class__ is not int and a.__class__ is not float and isinstance(a, Fraction)
    )
    b_is_fraction = (
        b.__class__ is not int and b.__class__ is not float and isinstance(b, Fraction)
    )
    if a_is_fraction and not b_is_fraction:
        b = maybe_simple_fraction(b)
    elif not a_is_fraction and b_is_fraction:
        a = maybe_simple_fraction(a)
    return a, b
