def evalf_log(expr, prec, options):
arg = expr.args[0]
workprec = prec + 10
xre, xim, xacc, _ = evalf(arg, workprec, options)
if xim:
# XXX: use get_abs etc instead
re = evalf_log(
C.log(C.Abs(arg, evaluate=False), evaluate=False), prec, options)
im = mpf_atan2(xim, xre or fzero, prec)
return re[0], im, re[2], prec
imaginary_term = (mpf_cmp(xre, fzero) < 0)
re = mpf_log(mpf_abs(xre), prec, rnd)
size = fastlog(re)
if prec - size > workprec:
# We actually need to compute 1+x accurately, not x
arg = C.Add(S.NegativeOne, arg, evaluate=False)
xre, xim, _, _ = evalf_add(arg, prec, options)
prec2 = workprec - fastlog(xre)
# xre is now x - 1 so we add 1 back here to calculate x
re = mpf_log(mpf_abs(mpf_add(xre, fone, prec2)), prec, rnd)
re_acc = prec
if imaginary_term:
return re, mpf_pi(prec), re_acc, prec
else:
return re, None, re_acc, None
def evalf_log(expr, prec, options):
arg = expr.args[0]
workprec = prec + 10
xre, xim, xacc, _ = evalf(arg, workprec, options)
if xim:
# XXX: use get_abs etc instead
re = evalf_log(C.log(C.Abs(arg, evaluate=False), evaluate=False), prec, options)
im = mpf_atan2(xim, xre or fzero, prec)
return re[0], im, re[2], prec
imaginary_term = mpf_cmp(xre, fzero) < 0
re = mpf_log(mpf_abs(xre), prec, rnd)
size = fastlog(re)
if prec - size > workprec:
# We actually need to compute 1+x accurately, not x
arg = C.Add(S.NegativeOne, arg, evaluate=False)
xre, xim, _, _ = evalf_add(arg, prec, options)
prec2 = workprec - fastlog(xre)
re = mpf_log(mpf_add(xre, fone, prec2), prec, rnd)
re_acc = prec
if imaginary_term:
return re, mpf_pi(prec), re_acc, prec
else:
return re, None, re_acc, None
def round(x, p=0):
"""Return x rounded to the given decimal place. If x is not an Expr,
Python's round function is employed.
Examples
========
>>> from sympy import round, pi, S, Number
>>> round(S(10.5))
11.
>>> round(pi)
3.
>>> round(pi, 2)
3.14
If x is not a SymPy Expr then Python's round is used and it returns
a Python type, not a SymPy Number:
>>> isinstance(round(543210, -2), Number)
False
>>> round(S(543210), -2)
5.432e+5
>>> _.is_Number
True
"""
from sympy.functions.elementary.exponential import log
from sympy.mpmath.libmp import prec_to_dps
if not isinstance(x, Expr):
return _pyround(x, p)
if not x.is_number:
raise TypeError('%s is not a number' % x)
if not x.is_real:
raise TypeError("can't convert complex to int")
if not x:
return x
p = int(p)
precs = [f._prec for f in x.atoms(C.Float)]
dps = prec_to_dps(max(precs)) if precs else None
xpos = abs(x.n())
try:
mag_first_dig = int(ceil(log10(xpos)))
except (ValueError, OverflowError):
mag_first_dig = int(ceil(C.Float(mpf_log(xpos._mpf_, 53))/log(10)))
# check that we aren't off by 1
if (xpos/10**mag_first_dig) >= 1:
mag_first_dig += 1
assert .1 <= (xpos/10**mag_first_dig) < 1
allow = digits_needed = mag_first_dig + p
if dps is not None and allow > dps:
allow = dps
mag = Pow(10, p) # magnitude needed to bring digit p to units place
x += 1/(2*mag) # add the half for rounding
i10 = 10*mag*x.n((dps if dps is not None else digits_needed) + 1)
rv = Integer(i10)//10
q = 1
if p > 0:
q = mag
elif p < 0:
rv /= mag
rv = Rational(rv, q)
if rv.is_Integer:
# use str or else it won't be a float
return C.Float(str(rv), digits_needed)
else:
return C.Float(rv, allow)
