# TRITIUM-PROVENANCE sha256=7d39c62b82a8fe24db8bfa1ad15f8cfe9b8cb789401717ec26e061c79bba383b lang=python
# TRITIUM-HEIGHT high=0.22 mid=0.59 low=0.19 fns=8
# TRITIUM-PSEUDO fn=fsin
#| fn fsin(x):
#|   return a * (1.0 + x2 * (-0.16666666666666666 + x2 * (0.008333333333333333 + x2 * (-0.0001984126984126984 + x2 * 2.7557319223985893e-06))))
# TRITIUM-HEIGHT fn=fsin high=0.00 mid=0.44 low=0.56 role=algo_mid
def fsin(x: float) -> float:
    pi = 3.141592653589793
    two = 6.283185307179586
    a = x
    while a > pi:
        a = a - two
    while a <= -pi:
        a = a + two
    x2 = a * a
    return a * (1.0 + x2 * (-0.16666666666666666 + x2 * (0.008333333333333333 + x2 * (-0.0001984126984126984 + x2 * 2.7557319223985893e-06))))

# TRITIUM-PSEUDO fn=fcos
#| fn fcos(x):
#|   return 1.0 + x2 * (-0.5 + x2 * (0.041666666666666664 + x2 * (-0.001388888888888889 + x2 * 2.48015873015873e-05)))
# TRITIUM-HEIGHT fn=fcos high=0.00 mid=0.44 low=0.56 role=algo_mid
def fcos(x: float) -> float:
    pi = 3.141592653589793
    two = 6.283185307179586
    a = x
    while a > pi:
        a = a - two
    while a <= -pi:
        a = a + two
    x2 = a * a
    return 1.0 + x2 * (-0.5 + x2 * (0.041666666666666664 + x2 * (-0.001388888888888889 + x2 * 2.48015873015873e-05)))

# TRITIUM-PSEUDO fn=fsqrt
#| fn fsqrt(x):
#|   return g
# TRITIUM-HEIGHT fn=fsqrt high=0.00 mid=0.63 low=0.37 role=algo_mid
def fsqrt(x: float) -> float:
    if x <= 0.0:
        return 0.0
    g = x
    i = 0
    while i < 8:
        g = 0.5 * (g + x / g)
        i = i + 1
    return g

# TRITIUM-PSEUDO fn=haversine_f
#| fn haversine_f(lat1, lon1, lat2, lon2):
#|   fsin(...)
#|   fsqrt(...)
#|   fcos(...)
#|   return 2.0 * fsqrt(h)
# TRITIUM-HEIGHT fn=haversine_f high=0.75 mid=0.25 low=0.00
def haversine_f(lat1: float, lon1: float, lat2: float, lon2: float) -> float:
    dlat = lat2 - lat1
    dlon = lon2 - lon1
    aa = fsin(dlat / 2.0)
    bb = fsin(dlon / 2.0)
    h = aa * aa + fcos(lat1) * fcos(lat2) * bb * bb
    return 2.0 * fsqrt(h)

# TRITIUM-PSEUDO fn=_atan_unit
#| fn _atan_unit(a):
#|   return r
# TRITIUM-HEIGHT fn=_atan_unit high=0.00 mid=1.00 low=0.00 role=algo_mid
def _atan_unit(a: float) -> float:
    t8 = 0.41421356237309503
    folded = 0
    t = a
    if t > t8:
        t = (1.0 - t) / (1.0 + t)
        folded = 1
    z2 = t * t
    r = t * (1.0 + z2 * (-0.3333333333333333 + z2 * (0.2 + z2 * (-0.14285714285714285 + z2 * (0.1111111111111111 + z2 * -0.09090909090909091)))))
    if folded == 1:
        r = 0.7853981633974483 - r
    return r

# TRITIUM-PSEUDO fn=fatan_poly
#| fn fatan_poly(z):
#|   _atan_unit(...)
#|   return r
# TRITIUM-HEIGHT fn=fatan_poly high=0.13 mid=0.87 low=0.00
def fatan_poly(z: float) -> float:
    neg = 0
    a = z
    if a < 0.0:
        a = 0.0 - a
        neg = 1
    swapped = 0
    if a > 1.0:
        a = 1.0 / a
        swapped = 1
    r = _atan_unit(a)
    if swapped == 1:
        r = 1.5707963267948966 - r
    if neg == 1:
        r = 0.0 - r
    return r

# TRITIUM-PSEUDO fn=fatan2
#| fn fatan2(y, x):
#|   fatan_poly(...)
# TRITIUM-HEIGHT fn=fatan2 high=0.19 mid=0.81 low=0.00 role=algo_mid
def fatan2(y: float, x: float) -> float:
    ay = y
    if ay < 0.0:
        ay = 0.0 - ay
    ax = x
    if ax < 0.0:
        ax = 0.0 - ax
    if ax >= ay:
        if ax == 0.0:
            return 0.0
        a = fatan_poly(ay / ax)
    else:
        if ay == 0.0:
            return 0.0
        a = 1.5707963267948966 - fatan_poly(ax / ay)
    if x < 0.0:
        if y < 0.0:
            return a - 3.141592653589793
        return 3.141592653589793 - a
    else:
        if y < 0.0:
            return 0.0 - a
        return a

# TRITIUM-PSEUDO fn=bearing_f
#| fn bearing_f(lat1, lon1, lat2, lon2):
#|   fsin(...)
#|   fcos(...)
#|   fatan2(...)
#|   return br
# TRITIUM-HEIGHT fn=bearing_f high=0.69 mid=0.31 low=0.00
def bearing_f(lat1: float, lon1: float, lat2: float, lon2: float) -> float:
    dlon = lon2 - lon1
    sd = fsin(dlon)
    cl2 = fcos(lat2)
    y = sd * cl2
    cl1 = fcos(lat1)
    sl2 = fsin(lat2)
    sl1 = fsin(lat1)
    cl2b = fcos(lat2)
    cd = fcos(dlon)
    x = cl1 * sl2 - sl1 * cl2b * cd
    br = fatan2(y, x)
    return br