def _apply_function_in_context(cls, f, args, context):
""" Apply an MPFR function 'f' to the given arguments 'args', rounding to
the given context. Returns a new Mpfr object with precision taken from
the current context.
"""
rounding = context.rounding
bf = mpfr.Mpfr_t.__new__(cls)
mpfr.mpfr_init2(bf, context.precision)
args = (bf,) + args + (rounding,)
ternary = f(*args)
with _temporary_exponent_bounds(context.emin, context.emax):
ternary = mpfr.mpfr_check_range(bf, ternary, rounding)
if context.subnormalize:
# mpfr_subnormalize doesn't set underflow and
# subnormal flags, so we do that ourselves. We choose
# to set the underflow flag for *all* cases where the
# 'after rounding' result is smaller than the smallest
# normal number, even if that result is exact.
# if bf is zero but ternary is nonzero, the underflow
# flag will already have been set by mpfr_check_range;
underflow = (
mpfr.mpfr_number_p(bf) and
not mpfr.mpfr_zero_p(bf) and
mpfr.mpfr_get_exp(bf) < context.precision - 1 + context.emin)
if underflow:
mpfr.mpfr_set_underflow()
ternary = mpfr.mpfr_subnormalize(bf, ternary, rounding)
if ternary:
mpfr.mpfr_set_inexflag()
return bf
def _apply_function_in_context(cls, f, args, context):
""" Apply an MPFR function 'f' to the given arguments 'args', rounding to
the given context. Returns a new Mpfr object with precision taken from
the current context.
"""
rounding = context.rounding
bf = mpfr.Mpfr_t.__new__(cls)
mpfr.mpfr_init2(bf, context.precision)
args = (bf,) + args + (rounding,)
ternary = f(*args)
with _temporary_exponent_bounds(context.emin, context.emax):
ternary = mpfr.mpfr_check_range(bf, ternary, rounding)
if context.subnormalize:
# mpfr_subnormalize doesn't set underflow and
# subnormal flags, so we do that ourselves. We choose
# to set the underflow flag for *all* cases where the
# 'after rounding' result is smaller than the smallest
# normal number, even if that result is exact.
# if bf is zero but ternary is nonzero, the underflow
# flag will already have been set by mpfr_check_range;
underflow = (
mpfr.mpfr_number_p(bf) and
not mpfr.mpfr_zero_p(bf) and
mpfr.mpfr_get_exp(bf) < context.precision - 1 + context.emin)
if underflow:
mpfr.mpfr_set_underflow()
ternary = mpfr.mpfr_subnormalize(bf, ternary, rounding)
if ternary:
mpfr.mpfr_set_inexflag()
return bf
def mpfr_mod(rop, x, y, rnd):
"""
Given two MPRF numbers x and y, compute
x - floor(x / y) * y, rounded if necessary using the given
rounding mode. The result is placed in 'rop'.
This is the 'remainder' operation, with sign convention
compatible with Python's % operator (where x % y has
the same sign as y).
"""
# There are various cases:
#
# 0. If either argument is a NaN, the result is NaN.
#
# 1. If x is infinite or y is zero, the result is NaN.
#
# 2. If y is infinite, return 0 with the sign of y if x is zero, x if x has
# the same sign as y, and infinity with the sign of y if it has the
# opposite sign.
#
# 3. If none of the above cases apply then both x and y are finite,
# and y is nonzero. If x and y have the same sign, simply
# return the result of fmod(x, y).
#
# 4. Now both x and y are finite, y is nonzero, and x and y have
# differing signs. Compute r = fmod(x, y) with sufficient precision
# to get an exact result. If r == 0, return 0 with the sign of y
# (which will be the opposite of the sign of x). If r != 0,
# return r + y, rounded appropriately.
if not mpfr.mpfr_number_p(x) or mpfr.mpfr_nan_p(y) or mpfr.mpfr_zero_p(y):
return mpfr.mpfr_fmod(rop, x, y, rnd)
elif mpfr.mpfr_inf_p(y):
x_negative = mpfr.mpfr_signbit(x)
y_negative = mpfr.mpfr_signbit(y)
if mpfr.mpfr_zero_p(x):
mpfr.mpfr_set_zero(rop, -y_negative)
return 0
elif x_negative == y_negative:
return mpfr.mpfr_set(rop, x, rnd)
else:
mpfr.mpfr_set_inf(rop, -y_negative)
return 0
x_negative = mpfr.mpfr_signbit(x)
y_negative = mpfr.mpfr_signbit(y)
if x_negative == y_negative:
return mpfr.mpfr_fmod(rop, x, y, rnd)
else:
p = max(mpfr.mpfr_get_prec(x), mpfr.mpfr_get_prec(y))
z = mpfr.Mpfr_t()
mpfr.mpfr_init2(z, p)
# Doesn't matter what rounding mode we use here; the result
# should be exact.
ternary = mpfr.mpfr_fmod(z, x, y, rnd)
assert ternary == 0
if mpfr.mpfr_zero_p(z):
mpfr.mpfr_set_zero(rop, -y_negative)
return 0
else:
return mpfr.mpfr_add(rop, y, z, rnd)
