import math
import sys

from rpython.rlib import rfloat
from rpython.rlib.objectmodel import specialize
from pypy.interpreter.error import OperationError, oefmt
from pypy.interpreter.gateway import unwrap_spec, WrappedDefault

class State:
    def __init__(self, space):
        self.w_e = space.newfloat(math.e)
        self.w_pi = space.newfloat(math.pi)
        self.w_inf = space.newfloat(rfloat.INFINITY)
        self.w_nan = space.newfloat(rfloat.NAN)
def get(space):
    return space.fromcache(State)

def _get_double(space, w_x):
    if space.is_w(space.type(w_x), space.w_float):
        return space.float_w(w_x)
    else:
        return space.float_w(space.float(w_x))

@specialize.arg(1)
def math1(space, f, w_x):
    x = _get_double(space, w_x)
    try:
        y = f(x)
    except OverflowError:
        raise oefmt(space.w_OverflowError, "math range error")
    except ValueError:
        raise oefmt(space.w_ValueError, "math domain error")
    return space.newfloat(y)

@specialize.arg(1)
def math1_w(space, f, w_x):
    x = _get_double(space, w_x)
    try:
        r = f(x)
    except OverflowError:
        raise oefmt(space.w_OverflowError, "math range error")
    except ValueError:
        raise oefmt(space.w_ValueError, "math domain error")
    return r

@specialize.arg(1)
def math2(space, f, w_x, w_snd):
    x = _get_double(space, w_x)
    snd = _get_double(space, w_snd)
    try:
        r = f(x, snd)
    except OverflowError:
        raise oefmt(space.w_OverflowError, "math range error")
    except ValueError:
        raise oefmt(space.w_ValueError, "math domain error")
    return space.newfloat(r)

def trunc(space, w_x):
    """Truncate x."""
    w_descr = space.lookup(w_x, '__trunc__')
    if w_descr is not None:
        return space.get_and_call_function(w_descr, w_x)
    return space.trunc(w_x)

def copysign(space, w_x, w_y):
    """Return x with the sign of y."""
    # No exceptions possible.
    x = _get_double(space, w_x)
    y = _get_double(space, w_y)
    return space.newfloat(math.copysign(x, y))

def isinf(space, w_x):
    """Return True if x is infinity."""
    return space.newbool(math.isinf(_get_double(space, w_x)))

def isnan(space, w_x):
    """Return True if x is not a number."""
    return space.newbool(math.isnan(_get_double(space, w_x)))

def isfinite(space, w_x):
    """isfinite(x) -> bool

    Return True if x is neither an infinity nor a NaN, and False otherwise."""
    return space.newbool(rfloat.isfinite(_get_double(space, w_x)))

def pow(space, w_x, w_y):
    """pow(x,y)

       Return x**y (x to the power of y).
    """
    return math2(space, math.pow, w_x, w_y)

def cosh(space, w_x):
    """cosh(x)

       Return the hyperbolic cosine of x.
    """
    return math1(space, math.cosh, w_x)

def ldexp(space, w_x,  w_i):
    """ldexp(x, i) -> x * (2**i)
    """
    x = _get_double(space, w_x)
    if space.isinstance_w(w_i, space.w_int):
        try:
            exp = space.int_w(w_i)
        except OperationError as e:
            if not e.match(space, space.w_OverflowError):
                raise
            if space.is_true(space.lt(w_i, space.newint(0))):
                exp = -sys.maxint
            else:
                exp = sys.maxint
    else:
        raise oefmt(space.w_TypeError, "integer required for second argument")
    try:
        r = math.ldexp(x, exp)
    except OverflowError:
        raise oefmt(space.w_OverflowError, "math range error")
    except ValueError:
        raise oefmt(space.w_ValueError, "math domain error")
    return space.newfloat(r)

def hypot(space, w_x, w_y):
    """hypot(x,y)

       Return the Euclidean distance, sqrt(x*x + y*y).
    """
    return math2(space, math.hypot, w_x, w_y)

def tan(space, w_x):
    """tan(x)

       Return the tangent of x (measured in radians).
    """
    return math1(space, math.tan, w_x)

def asin(space, w_x):
    """asin(x)

       Return the arc sine (measured in radians) of x.
    """
    return math1(space, math.asin, w_x)

def fabs(space, w_x):
    """fabs(x)

       Return the absolute value of the float x.
    """
    return math1(space, math.fabs, w_x)

def floor(space, w_x):
    """floor(x)

       Return the floor of x as an int.
       This is the largest integral value <= x.
    """
    from pypy.objspace.std.longobject import newlong_from_float
    w_descr = space.lookup(w_x, '__floor__')
    if w_descr is not None:
        return space.get_and_call_function(w_descr, w_x)
    x = _get_double(space, w_x)
    return newlong_from_float(space, math.floor(x))

def sqrt(space, w_x):
    """sqrt(x)

       Return the square root of x.
    """
    return math1(space, math.sqrt, w_x)

def frexp(space, w_x):
    """frexp(x)

       Return the mantissa and exponent of x, as pair (m, e).
       m is a float and e is an int, such that x = m * 2.**e.
       If x is 0, m and e are both 0.  Else 0.5 <= abs(m) < 1.0.
    """
    mant, expo = math1_w(space, math.frexp, w_x)
    return space.newtuple([space.newfloat(mant), space.newint(expo)])

degToRad = math.pi / 180.0

def degrees(space, w_x):
    """degrees(x) -> converts angle x from radians to degrees
    """
    return space.newfloat(_get_double(space, w_x) / degToRad)

def _log_any(space, w_x, base):
    # base is supposed to be positive or 0.0, which means we use e
    try:
        try:
            x = _get_double(space, w_x)
        except OperationError as e:
            if not e.match(space, space.w_OverflowError):
                raise
            if not space.isinstance_w(w_x, space.w_int):
                raise
            # special case to support log(extremely-large-long)
            num = space.bigint_w(w_x)
            result = num.log(base)
        else:
            if base == 10.0:
                result = math.log10(x)
            elif base == 2.0:
                result = rfloat.log2(x)
            else:
                result = math.log(x)
                if base != 0.0:
                    den = math.log(base)
                    result /= den
    except OverflowError:
        raise oefmt(space.w_OverflowError, "math range error")
    except ValueError:
        raise oefmt(space.w_ValueError, "math domain error")
    return space.newfloat(result)

def log(space, w_x, w_base=None):
    """log(x[, base]) -> the logarithm of x to the given base.
       If the base not specified, returns the natural logarithm (base e) of x.
    """
    if w_base is None:
        base = 0.0
    else:
        base = _get_double(space, w_base)
        if base <= 0.0:
            # just for raising the proper errors
            return math1(space, math.log, w_base)
    return _log_any(space, w_x, base)

def log2(space, w_x):
    """log2(x) -> the base 2 logarithm of x.
    """
    return _log_any(space, w_x, 2.0)

def log10(space, w_x):
    """log10(x) -> the base 10 logarithm of x.
    """
    return _log_any(space, w_x, 10.0)

def fmod(space, w_x, w_y):
    """fmod(x,y)

       Return fmod(x, y), according to platform C.  x % y may differ.
    """
    return math2(space, math.fmod, w_x, w_y)

def atan(space, w_x):
    """atan(x)

       Return the arc tangent (measured in radians) of x.
    """
    return math1(space, math.atan, w_x)

def ceil(space, w_x):
    """ceil(x)

       Return the ceiling of x as an int.
       This is the smallest integral value >= x.
    """
    from pypy.objspace.std.longobject import newlong_from_float
    w_descr = space.lookup(w_x, '__ceil__')
    if w_descr is not None:
        return space.get_and_call_function(w_descr, w_x)
    return newlong_from_float(space, math1_w(space, math.ceil, w_x))

def sinh(space, w_x):
    """sinh(x)

       Return the hyperbolic sine of x.
    """
    return math1(space, math.sinh, w_x)

def cos(space, w_x):
    """cos(x)

       Return the cosine of x (measured in radians).
    """
    return math1(space, math.cos, w_x)

def tanh(space, w_x):
    """tanh(x)

       Return the hyperbolic tangent of x.
    """
    return math1(space, math.tanh, w_x)

def radians(space, w_x):
    """radians(x) -> converts angle x from degrees to radians
    """
    return space.newfloat(_get_double(space, w_x) * degToRad)

def sin(space, w_x):
    """sin(x)

       Return the sine of x (measured in radians).
    """
    return math1(space, math.sin, w_x)

def atan2(space, w_y, w_x):
    """atan2(y, x)

       Return the arc tangent (measured in radians) of y/x.
       Unlike atan(y/x), the signs of both x and y are considered.
    """
    return math2(space, math.atan2, w_y,  w_x)

def modf(space, w_x):
    """modf(x)

       Return the fractional and integer parts of x.  Both results carry the sign
       of x.  The integer part is returned as a real.
    """
    frac, intpart = math1_w(space, math.modf, w_x)
    return space.newtuple([space.newfloat(frac), space.newfloat(intpart)])

def exp(space, w_x):
    """exp(x)

       Return e raised to the power of x.
    """
    return math1(space, math.exp, w_x)

def acos(space, w_x):
    """acos(x)

       Return the arc cosine (measured in radians) of x.
    """
    return math1(space, math.acos, w_x)

def fsum(space, w_iterable):
    """Sum an iterable of floats, trying to keep precision."""
    w_iter = space.iter(w_iterable)
    inf_sum = special_sum = 0.0
    partials = []
    while True:
        try:
            w_value = space.next(w_iter)
        except OperationError as e:
            if not e.match(space, space.w_StopIteration):
                raise
            break
        v = _get_double(space, w_value)
        original = v
        added = 0
        for y in partials:
            if abs(v) < abs(y):
                v, y = y, v
            hi = v + y
            yr = hi - v
            lo = y - yr
            if lo != 0.0:
                partials[added] = lo
                added += 1
            v = hi
        del partials[added:]
        if v != 0.0:
            if not rfloat.isfinite(v):
                if rfloat.isfinite(original):
                    raise oefmt(space.w_OverflowError, "intermediate overflow")
                if math.isinf(original):
                    inf_sum += original
                special_sum += original
                del partials[:]
            else:
                partials.append(v)
    if special_sum != 0.0:
        if math.isnan(inf_sum):
            raise oefmt(space.w_ValueError, "-inf + inf")
        return space.newfloat(special_sum)
    hi = 0.0
    if partials:
        hi = partials[-1]
        j = 0
        lo = 0
        for j in range(len(partials) - 2, -1, -1):
            v = hi
            y = partials[j]
            assert abs(y) < abs(v)
            hi = v + y
            yr = hi - v
            lo = y - yr
            if lo != 0.0:
                break
        if j > 0 and (lo < 0.0 and partials[j - 1] < 0.0 or
                      lo > 0.0 and partials[j - 1] > 0.0):
            y = lo * 2.0
            v = hi + y
            yr = v - hi
            if y == yr:
                hi = v
    return space.newfloat(hi)

def log1p(space, w_x):
    """Find log(x + 1)."""
    try:
        return math1(space, rfloat.log1p, w_x)
    except OperationError as e:
        # Python 2.x (and thus ll_math) raises a OverflowError improperly.
        if not e.match(space, space.w_OverflowError):
            raise
        raise oefmt(space.w_ValueError, "math domain error")

def acosh(space, w_x):
    """Inverse hyperbolic cosine"""
    return math1(space, rfloat.acosh, w_x)

def asinh(space, w_x):
    """Inverse hyperbolic sine"""
    return math1(space, rfloat.asinh, w_x)

def atanh(space, w_x):
    """Inverse hyperbolic tangent"""
    return math1(space, rfloat.atanh, w_x)

def expm1(space, w_x):
    """exp(x) - 1"""
    return math1(space, rfloat.expm1, w_x)

def erf(space, w_x):
    """The error function"""
    return math1(space, rfloat.erf, w_x)

def erfc(space, w_x):
    """The complementary error function"""
    return math1(space, rfloat.erfc, w_x)

def gamma(space, w_x):
    """Compute the gamma function for x."""
    return math1(space, rfloat.gamma, w_x)

def lgamma(space, w_x):
    """Compute the natural logarithm of the gamma function for x."""
    return math1(space, rfloat.lgamma, w_x)

@unwrap_spec(w_rel_tol=WrappedDefault(1e-09), w_abs_tol=WrappedDefault(0.0))
def isclose(space, w_a, w_b, __kwonly__, w_rel_tol, w_abs_tol):
    """isclose(a, b, *, rel_tol=1e-09, abs_tol=0.0) -> bool

Determine whether two floating point numbers are close in value.

   rel_tol
       maximum difference for being considered "close", relative to the
       magnitude of the input values
   abs_tol
       maximum difference for being considered "close", regardless of the
       magnitude of the input values

Return True if a is close in value to b, and False otherwise.

For the values to be considered close, the difference between them
must be smaller than at least one of the tolerances.

-inf, inf and NaN behave similarly to the IEEE 754 Standard.  That
is, NaN is not close to anything, even itself.  inf and -inf are
only close to themselves."""
    a = _get_double(space, w_a)
    b = _get_double(space, w_b)
    rel_tol = _get_double(space, w_rel_tol)
    abs_tol = _get_double(space, w_abs_tol)
    #
    # sanity check on the inputs
    if rel_tol < 0.0 or abs_tol < 0.0:
        raise oefmt(space.w_ValueError, "tolerances must be non-negative")
    #
    # short circuit exact equality -- needed to catch two infinities of
    # the same sign. And perhaps speeds things up a bit sometimes.
    if a == b:
        return space.w_True
    #
    # This catches the case of two infinities of opposite sign, or
    # one infinity and one finite number. Two infinities of opposite
    # sign would otherwise have an infinite relative tolerance.
    # Two infinities of the same sign are caught by the equality check
    # above.
    if math.isinf(a) or math.isinf(b):
        return space.w_False
    #
    # now do the regular computation
    # this is essentially the "weak" test from the Boost library
    diff = math.fabs(b - a)
    result = ((diff <= math.fabs(rel_tol * b) or
               diff <= math.fabs(rel_tol * a)) or
              diff <= abs_tol)
    return space.newbool(result)