cmath.py 文件源码

def asinh(x):
    _asinh_special = [
        [-inf-1j*pi/4, complex(-float("inf"), -0.0), complex(-float("inf"), -0.0),
            complex(-float("inf"), 0.0), complex(-float("inf"), 0.0), -inf+1j*pi/4, -inf+nanj],
        [-inf-1j*pi/2, None, None, None, None, -inf+1j*pi/2, nan+nanj],
        [-inf-1j*pi/2, None, None, None, None, -inf+1j*pi/2, nan+nanj],
        [inf-1j*pi/2, None, None, None, None, inf+1j*pi/2, nan+nanj],
        [inf-1j*pi/2, None, None, None, None, inf+1j*pi/2, nan+nanj],
        [inf-1j*pi/4, complex(float("inf"), -0.0), complex(float("inf"), -0.0),
            inf, inf, inf+1j*pi/4, inf+nanj],
        [inf+nanj, nan+nanj, complex(float("nan"), -0.0), nan, nan+nanj, inf+nanj, nan+nanj]
    ]

    z = _make_complex(x)

    if not isfinite(z):
        return _asinh_special[_special_type(z.real)][_special_type(z.imag)]

    if abs(z.real) > _LARGE_DOUBLE or abs(z.imag) > _LARGE_DOUBLE:
        if z.imag >= 0:
            real = math.copysign(math.log(math.hypot(z.imag/2, z.real/2)) +
                                 2 * _LOG_2, z.real)
        else:
            real = -math.copysign(math.log(math.hypot(z.imag/2, z.real/2)) +
                                  2 * _LOG_2, -z.real)
        return complex(real, math.atan2(z.imag, abs(z.real)))

    s1 = sqrt(complex(1+z.imag, -z.real))
    s2 = sqrt(complex(1-z.imag, z.real))
    return complex(math.asinh(s1.real*s2.imag-s2.real*s1.imag),
                   math.atan2(z.imag, s1.real*s2.real - s1.imag*s2.imag))