def c_acosh(x, y):
# XXX the following two lines seem unnecessary at least on Linux;
# the tests pass fine without them
if not isfinite(x) or not isfinite(y):
return acosh_special_values[special_type(x)][special_type(y)]
if fabs(x) > CM_LARGE_DOUBLE or fabs(y) > CM_LARGE_DOUBLE:
# avoid unnecessary overflow for large arguments
real = math.log(math.hypot(x/2., y/2.)) + M_LN2*2.
imag = math.atan2(y, x)
else:
s1x, s1y = c_sqrt(x - 1., y)
s2x, s2y = c_sqrt(x + 1., y)
real = asinh(s1x*s2x + s1y*s2y)
imag = 2.*math.atan2(s1y, s2x)
return (real, imag)
def c_acosh(x, y):
# XXX the following two lines seem unnecessary at least on Linux;
# the tests pass fine without them
if not isfinite(x) or not isfinite(y):
return acosh_special_values[special_type(x)][special_type(y)]
if fabs(x) > CM_LARGE_DOUBLE or fabs(y) > CM_LARGE_DOUBLE:
# avoid unnecessary overflow for large arguments
real = math.log(math.hypot(x / 2., y / 2.)) + M_LN2 * 2.
imag = math.atan2(y, x)
else:
s1x, s1y = c_sqrt(x - 1., y)
s2x, s2y = c_sqrt(x + 1., y)
real = asinh(s1x * s2x + s1y * s2y)
imag = 2. * math.atan2(s1y, s2x)
return (real, imag)
def c_asinh(x, y):
if not isfinite(x) or not isfinite(y):
return asinh_special_values[special_type(x)][special_type(y)]
if fabs(x) > CM_LARGE_DOUBLE or fabs(y) > CM_LARGE_DOUBLE:
if y >= 0.:
real = copysign(math.log(math.hypot(x/2., y/2.)) +
M_LN2*2., x)
else:
real = -copysign(math.log(math.hypot(x/2., y/2.)) +
M_LN2*2., -x)
imag = math.atan2(y, fabs(x))
else:
s1x, s1y = c_sqrt(1.+y, -x)
s2x, s2y = c_sqrt(1.-y, x)
real = asinh(s1x*s2y - s2x*s1y)
imag = math.atan2(y, s1x*s2x - s1y*s2y)
return (real, imag)
def c_asinh(x, y):
if not isfinite(x) or not isfinite(y):
return asinh_special_values[special_type(x)][special_type(y)]
if fabs(x) > CM_LARGE_DOUBLE or fabs(y) > CM_LARGE_DOUBLE:
if y >= 0.:
real = copysign(
math.log(math.hypot(x / 2., y / 2.)) + M_LN2 * 2., x)
else:
real = -copysign(
math.log(math.hypot(x / 2., y / 2.)) + M_LN2 * 2., -x)
imag = math.atan2(y, fabs(x))
else:
s1x, s1y = c_sqrt(1. + y, -x)
s2x, s2y = c_sqrt(1. - y, x)
real = asinh(s1x * s2y - s2x * s1y)
imag = math.atan2(y, s1x * s2x - s1y * s2y)
return (real, imag)
def c_acos(x, y):
if not isfinite(x) or not isfinite(y):
return acos_special_values[special_type(x)][special_type(y)]
if fabs(x) > CM_LARGE_DOUBLE or fabs(y) > CM_LARGE_DOUBLE:
# avoid unnecessary overflow for large arguments
real = math.atan2(fabs(y), x)
# split into cases to make sure that the branch cut has the
# correct continuity on systems with unsigned zeros
if x < 0.:
imag = -copysign(math.log(math.hypot(x/2., y/2.)) +
M_LN2*2., y)
else:
imag = copysign(math.log(math.hypot(x/2., y/2.)) +
M_LN2*2., -y)
else:
s1x, s1y = c_sqrt(1.-x, -y)
s2x, s2y = c_sqrt(1.+x, y)
real = 2.*math.atan2(s1x, s2x)
imag = asinh(s2x*s1y - s2y*s1x)
return (real, imag)
def c_acos(x, y):
if not isfinite(x) or not isfinite(y):
return acos_special_values[special_type(x)][special_type(y)]
if fabs(x) > CM_LARGE_DOUBLE or fabs(y) > CM_LARGE_DOUBLE:
# avoid unnecessary overflow for large arguments
real = math.atan2(fabs(y), x)
# split into cases to make sure that the branch cut has the
# correct continuity on systems with unsigned zeros
if x < 0.:
imag = -copysign(
math.log(math.hypot(x / 2., y / 2.)) + M_LN2 * 2., y)
else:
imag = copysign(
math.log(math.hypot(x / 2., y / 2.)) + M_LN2 * 2., -y)
else:
s1x, s1y = c_sqrt(1. - x, -y)
s2x, s2y = c_sqrt(1. + x, y)
real = 2. * math.atan2(s1x, s2x)
imag = asinh(s2x * s1y - s2y * s1x)
return (real, imag)