def mpi_atan2(y, x, prec):
ya, yb = y
xa, xb = x
# Constrained to the real line
if ya == yb == fzero:
if mpf_ge(xa, fzero):
return mpi_zero
return mpi_pi(prec)
# Right half-plane
if mpf_ge(xa, fzero):
if mpf_ge(ya, fzero):
a = mpf_atan2(ya, xb, prec, round_floor)
else:
a = mpf_atan2(ya, xa, prec, round_floor)
if mpf_ge(yb, fzero):
b = mpf_atan2(yb, xa, prec, round_ceiling)
else:
b = mpf_atan2(yb, xb, prec, round_ceiling)
# Upper half-plane
elif mpf_ge(ya, fzero):
b = mpf_atan2(ya, xa, prec, round_ceiling)
if mpf_le(xb, fzero):
a = mpf_atan2(yb, xb, prec, round_floor)
else:
a = mpf_atan2(ya, xb, prec, round_floor)
# Lower half-plane
elif mpf_le(yb, fzero):
a = mpf_atan2(yb, xa, prec, round_floor)
if mpf_le(xb, fzero):
b = mpf_atan2(ya, xb, prec, round_ceiling)
else:
b = mpf_atan2(yb, xb, prec, round_ceiling)
# Covering the origin
else:
b = mpf_pi(prec, round_ceiling)
a = mpf_neg(b)
return a, b
def mpi_atan2(y, x, prec):
ya, yb = y
xa, xb = x
# Constrained to the real line
if ya == yb == fzero:
if mpf_ge(xa, fzero):
return mpi_zero
return mpi_pi(prec)
# Right half-plane
if mpf_ge(xa, fzero):
if mpf_ge(ya, fzero):
a = mpf_atan2(ya, xb, prec, round_floor)
else:
a = mpf_atan2(ya, xa, prec, round_floor)
if mpf_ge(yb, fzero):
b = mpf_atan2(yb, xa, prec, round_ceiling)
else:
b = mpf_atan2(yb, xb, prec, round_ceiling)
# Upper half-plane
elif mpf_ge(ya, fzero):
b = mpf_atan2(ya, xa, prec, round_ceiling)
if mpf_le(xb, fzero):
a = mpf_atan2(yb, xb, prec, round_floor)
else:
a = mpf_atan2(ya, xb, prec, round_floor)
# Lower half-plane
elif mpf_le(yb, fzero):
a = mpf_atan2(yb, xa, prec, round_floor)
if mpf_le(xb, fzero):
b = mpf_atan2(ya, xb, prec, round_ceiling)
else:
b = mpf_atan2(yb, xb, prec, round_ceiling)
# Covering the origin
else:
b = mpf_pi(prec, round_ceiling)
a = mpf_neg(b)
return a, b
def mpc_arg(z, prec, rnd=round_fast):
"""Argument of a complex number. Returns an mpf value."""
a, b = z
return mpf_atan2(b, a, prec, rnd)
return mpf_pos(a, prec, rnd), mpf_pos(b, prec, rnd)
def mpc_neg((a, b), prec=None, rnd=round_fast):
return mpf_neg(a, prec, rnd), mpf_neg(b, prec, rnd)
def mpc_shift((a, b), n):
return mpf_shift(a, n), mpf_shift(b, n)
def mpc_abs((a, b), prec, rnd=round_fast):
"""Absolute value of a complex number, |a+bi|.
Returns an mpf value."""
return mpf_hypot(a, b, prec, rnd)
def mpc_arg((a, b), prec, rnd=round_fast):
"""Argument of a complex number. Returns an mpf value."""
return mpf_atan2(b, a, prec, rnd)
def mpc_floor((a, b), prec, rnd=round_fast):
return mpf_floor(a, prec, rnd), mpf_floor(b, prec, rnd)
def mpc_ceil((a, b), prec, rnd=round_fast):
return mpf_ceil(a, prec, rnd), mpf_ceil(b, prec, rnd)
def mpc_mul((a, b), (c, d), prec, rnd=round_fast):
"""Complex multiplication.
Returns the real and imaginary part of (a+bi)*(c+di), rounded to
the specified precision. The rounding mode applies to the real and
imaginary parts separately."""
asign, aman, aexp, abc = a
def atan2(ctx, y, x):
x = ctx.convert(x)
y = ctx.convert(y)
return ctx.make_mpf(libelefun.mpf_atan2(y._mpf_, x._mpf_, *ctx._prec_rounding))
def atan2(y,x):
"""atan2(y, x) has the same magnitude as atan(y/x) but accounts for
the signs of y and x. (Defined for real x and y only.)"""
x = convert_lossless(x)
y = convert_lossless(y)
return make_mpf(libelefun.mpf_atan2(y._mpf_, x._mpf_, *prec_rounding))
return mpf_neg(a, prec, rnd), mpf_neg(b, prec, rnd)
def mpc_shift((a, b), n):
return mpf_shift(a, n), mpf_shift(b, n)
def mpc_abs((a, b), prec, rnd=round_fast):
"""Absolute value of a complex number, |a+bi|.
Returns an mpf value."""
return mpf_hypot(a, b, prec, rnd)
def mpc_arg((a, b), prec, rnd=round_fast):
"""Argument of a complex number. Returns an mpf value."""
return mpf_atan2(b, a, prec, rnd)
def mpc_floor((a, b), prec, rnd=round_fast):
return mpf_floor(a, prec, rnd), mpf_floor(b, prec, rnd)
def mpc_ceil((a, b), prec, rnd=round_fast):
return mpf_ceil(a, prec, rnd), mpf_ceil(b, prec, rnd)
def mpc_mul((a, b), (c, d), prec, rnd=round_fast):
"""Complex multiplication.
Returns the real and imaginary part of (a+bi)*(c+di), rounded to
the specified precision. The rounding mode applies to the real and
def mpc_arg(z, prec, rnd=round_fast):
"""Argument of a complex number. Returns an mpf value."""
a, b = z
return mpf_atan2(b, a, prec, rnd)
def atan2(y, x):
"""atan2(y, x) has the same magnitude as atan(y/x) but accounts for
the signs of y and x. (Defined for real x and y only.)"""
x = convert_lossless(x)
y = convert_lossless(y)
return make_mpf(libelefun.mpf_atan2(y._mpf_, x._mpf_, *prec_rounding))
def atan2(ctx, y, x):
x = ctx.convert(x)
y = ctx.convert(y)
return ctx.make_mpf(
libelefun.mpf_atan2(y._mpf_, x._mpf_, *ctx._prec_rounding))
