Example #1
0
def exp(x, err=defaultError):
    """
    exp(x [,err]) is the exponential function.
    """
    try:
        rx = rational.Rational(x)
        if isinstance(err, RelativeError):
            _err = real.RelativeError(0, err.relativeerrorrange)
        elif isinstance(err, AbsoluteError):
            _err = real.AbsoluteError(0, err.absoluteerrorrange)
        return real.exp(rx, _err)
    except TypeError:
        pass
    if (defaultError >= err) or isinstance(err, AbsoluteError):
        # divide real part and imaginary part
        if isinstance(err, RelativeError):
            _err = real.RelativeError(0, err.relativeerrorrange, 2)
        elif isinstance(err, AbsoluteError):
            _err = real.AbsoluteError(0, err.absoluteerrorrange, 2)
        radius = real.exp(x.real, _err)
        if isinstance(err, RelativeError):
            _err = RelativeError(err.relativeerrorrange / 2)
        elif isinstance(err, AbsoluteError):
            _err = AbsoluteError(err.absoluteerrorrange / 2)
        arg = expi(x.imag, _err)
        return radius * arg
    else:
        return Complex(cmath.exp(complex(x.real,x.imag)))
Example #2
0
def expi(x, err=defaultError):
    """
    expi(x [,err]) returns exp(i * x) where i is the imaginary unit
    and x must be a real number.
    """
    if x == 0:
        return rational.Integer(1)
    if isinstance(err, RelativeError):
        _err = real.RelativeError(0, err.relativeerrorrange, 2)
    elif isinstance(err, AbsoluteError):
        _err = real.AbsoluteError(0, err.absoluteerrorrange, 2)
    re = real.cos(x, _err)
    im = real.sin(x, _err)
    return Complex(re, im)
Example #3
0
def log(x, err=defaultError):
    """
    log(x [,err]) returns the natural logarithm of x. There is one
    branch cut, from 0 along the negative real axis to -infinity,
    continuous from above.
    """
    if (defaultError >= err) or isinstance(err, AbsoluteError):
        if isinstance(err, RelativeError):
            _err = real.RelativeError(0, err.relativeerrorrange, 2)
        elif isinstance(err, AbsoluteError):
            _err = real.AbsoluteError(0, err.absoluteerrorrange, 2)
        if x in real.theRealField:
            x = +x
            if x > 0:
                return real.log(x, err=_err)
            elif x < 0:
                return Complex(real.log(abs(x), _err), real.pi(_err))
        return Complex(real.log(abs(x), err=_err), real.atan2(x.imag, x.real, _err))
    else:
        return Complex(cmath.log(complex(x.real, x.imag)))