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)))
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)
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)))