def c_cosh(x, y):
if not isfinite(x) or not isfinite(y):
if isinf(x) and isfinite(y) and y != 0.:
if x > 0:
real = copysign(INF, math.cos(y))
imag = copysign(INF, math.sin(y))
else:
real = copysign(INF, math.cos(y))
imag = -copysign(INF, math.sin(y))
r = (real, imag)
else:
r = cosh_special_values[special_type(x)][special_type(y)]
# need to raise ValueError if y is +/- infinity and x is not
# a NaN
if isinf(y) and not isnan(x):
raise ValueError("math domain error")
return r
if fabs(x) > CM_LOG_LARGE_DOUBLE:
# deal correctly with cases where cosh(x) overflows but
# cosh(z) does not.
x_minus_one = x - copysign(1., x)
real = math.cos(y) * math.cosh(x_minus_one) * math.e
imag = math.sin(y) * math.sinh(x_minus_one) * math.e
else:
real = math.cos(y) * math.cosh(x)
imag = math.sin(y) * math.sinh(x)
if isinf(real) or isinf(imag):
raise OverflowError("math range error")
return real, imag
def c_atanh(x, y):
if not isfinite(x) or not isfinite(y):
return atanh_special_values[special_type(x)][special_type(y)]
# Reduce to case where x >= 0., using atanh(z) = -atanh(-z).
if x < 0.:
return c_neg(*c_atanh(*c_neg(x, y)))
ay = fabs(y)
if x > CM_SQRT_LARGE_DOUBLE or ay > CM_SQRT_LARGE_DOUBLE:
# if abs(z) is large then we use the approximation
# atanh(z) ~ 1/z +/- i*pi/2 (+/- depending on the sign
# of y
h = math.hypot(x / 2., y / 2.) # safe from overflow
real = x / 4. / h / h
# the two negations in the next line cancel each other out
# except when working with unsigned zeros: they're there to
# ensure that the branch cut has the correct continuity on
# systems that don't support signed zeros
imag = -copysign(math.pi / 2., -y)
elif x == 1. and ay < CM_SQRT_DBL_MIN:
# C99 standard says: atanh(1+/-0.) should be inf +/- 0i
if ay == 0.:
raise ValueError("math domain error")
#real = INF
#imag = y
else:
real = -math.log(math.sqrt(ay) / math.sqrt(math.hypot(ay, 2.)))
imag = copysign(math.atan2(2., -ay) / 2, y)
else:
real = log1p(4. * x / ((1 - x) * (1 - x) + ay * ay)) / 4.
imag = -math.atan2(-2. * y, (1 - x) * (1 + x) - ay * ay) / 2.
return (real, imag)
def c_exp(x, y):
if not isfinite(x) or not isfinite(y):
if isinf(x) and isfinite(y) and y != 0.:
if x > 0:
real = copysign(INF, math.cos(y))
imag = copysign(INF, math.sin(y))
else:
real = copysign(0., math.cos(y))
imag = copysign(0., math.sin(y))
r = (real, imag)
else:
r = exp_special_values[special_type(x)][special_type(y)]
# need to raise ValueError if y is +/- infinity and x is not
# a NaN and not -infinity
if isinf(y) and (isfinite(x) or (isinf(x) and x > 0)):
raise ValueError("math domain error")
return r
if x > CM_LOG_LARGE_DOUBLE:
l = math.exp(x - 1.)
real = l * math.cos(y) * math.e
imag = l * math.sin(y) * math.e
else:
l = math.exp(x)
real = l * math.cos(y)
imag = l * math.sin(y)
if isinf(real) or isinf(imag):
raise OverflowError("math range error")
return real, imag
def c_cosh(x, y):
if not isfinite(x) or not isfinite(y):
if isinf(x) and isfinite(y) and y != 0.:
if x > 0:
real = copysign(INF, math.cos(y))
imag = copysign(INF, math.sin(y))
else:
real = copysign(INF, math.cos(y))
imag = -copysign(INF, math.sin(y))
r = (real, imag)
else:
r = cosh_special_values[special_type(x)][special_type(y)]
# need to raise ValueError if y is +/- infinity and x is not
# a NaN
if isinf(y) and not isnan(x):
raise ValueError("math domain error")
return r
if fabs(x) > CM_LOG_LARGE_DOUBLE:
# deal correctly with cases where cosh(x) overflows but
# cosh(z) does not.
x_minus_one = x - copysign(1., x)
real = math.cos(y) * math.cosh(x_minus_one) * math.e
imag = math.sin(y) * math.sinh(x_minus_one) * math.e
else:
real = math.cos(y) * math.cosh(x)
imag = math.sin(y) * math.sinh(x)
if isinf(real) or isinf(imag):
raise OverflowError("math range error")
return real, imag
def c_exp(x, y):
if not isfinite(x) or not isfinite(y):
if isinf(x) and isfinite(y) and y != 0.:
if x > 0:
real = copysign(INF, math.cos(y))
imag = copysign(INF, math.sin(y))
else:
real = copysign(0., math.cos(y))
imag = copysign(0., math.sin(y))
r = (real, imag)
else:
r = exp_special_values[special_type(x)][special_type(y)]
# need to raise ValueError if y is +/- infinity and x is not
# a NaN and not -infinity
if isinf(y) and (isfinite(x) or (isinf(x) and x > 0)):
raise ValueError("math domain error")
return r
if x > CM_LOG_LARGE_DOUBLE:
l = math.exp(x-1.)
real = l * math.cos(y) * math.e
imag = l * math.sin(y) * math.e
else:
l = math.exp(x)
real = l * math.cos(y)
imag = l * math.sin(y)
if isinf(real) or isinf(imag):
raise OverflowError("math range error")
return real, imag
def c_sinh(x, y):
# special treatment for sinh(+/-inf + iy) if y is finite and nonzero
if not isfinite(x) or not isfinite(y):
if isinf(x) and isfinite(y) and y != 0.:
if x > 0:
real = copysign(INF, math.cos(y))
imag = copysign(INF, math.sin(y))
else:
real = -copysign(INF, math.cos(y))
imag = copysign(INF, math.sin(y))
r = (real, imag)
else:
r = sinh_special_values[special_type(x)][special_type(y)]
# need to raise ValueError if y is +/- infinity and x is not
# a NaN
if isinf(y) and not isnan(x):
raise ValueError("math domain error")
return r
if fabs(x) > CM_LOG_LARGE_DOUBLE:
x_minus_one = x - copysign(1., x)
real = math.cos(y) * math.sinh(x_minus_one) * math.e
imag = math.sin(y) * math.cosh(x_minus_one) * math.e
else:
real = math.cos(y) * math.sinh(x)
imag = math.sin(y) * math.cosh(x)
if isinf(real) or isinf(imag):
raise OverflowError("math range error")
return real, imag
def c_rect(r, phi):
if not isfinite(r) or not isfinite(phi):
# if r is +/-infinity and phi is finite but nonzero then
# result is (+-INF +-INF i), but we need to compute cos(phi)
# and sin(phi) to figure out the signs.
if isinf(r) and isfinite(phi) and phi != 0.:
if r > 0:
real = copysign(INF, math.cos(phi))
imag = copysign(INF, math.sin(phi))
else:
real = -copysign(INF, math.cos(phi))
imag = -copysign(INF, math.sin(phi))
z = (real, imag)
else:
z = rect_special_values[special_type(r)][special_type(phi)]
# need to raise ValueError if r is a nonzero number and phi
# is infinite
if r != 0. and not isnan(r) and isinf(phi):
raise ValueError("math domain error")
return z
real = r * math.cos(phi)
imag = r * math.sin(phi)
return real, imag
def str__Complex(space, w_complex):
if w_complex.realval == 0 and copysign(1., w_complex.realval) == 1.:
return space.wrap(str_format(w_complex.imagval) + 'j')
sign = (copysign(1., w_complex.imagval) == 1. or
isnan(w_complex.imagval)) and '+' or ''
return space.wrap('(' + str_format(w_complex.realval)
+ sign + str_format(w_complex.imagval) + 'j)')
def test_nan_and_special_values():
from pypy.rlib.rfloat import isnan, isinf, isfinite, copysign
inf = 1e300 * 1e300
assert isinf(inf)
nan = inf/inf
assert isnan(nan)
for value, checker in [
(inf, lambda x: isinf(x) and x > 0.0),
(-inf, lambda x: isinf(x) and x < 0.0),
(nan, isnan),
(42.0, isfinite),
(0.0, lambda x: not x and copysign(1., x) == 1.),
(-0.0, lambda x: not x and copysign(1., x) == -1.),
]:
def f():
return value
f1 = compile(f, [])
res = f1()
assert checker(res)
l = [value]
def g(x):
return l[x]
g2 = compile(g, [int])
res = g2(0)
assert checker(res)
l2 = [(-value, -value), (value, value)]
def h(x):
return l2[x][1]
h3 = compile(h, [int])
res = h3(1)
assert checker(res)
def c_atanh(x, y):
if not isfinite(x) or not isfinite(y):
return atanh_special_values[special_type(x)][special_type(y)]
# Reduce to case where x >= 0., using atanh(z) = -atanh(-z).
if x < 0.:
return c_neg(*c_atanh(*c_neg(x, y)))
ay = fabs(y)
if x > CM_SQRT_LARGE_DOUBLE or ay > CM_SQRT_LARGE_DOUBLE:
# if abs(z) is large then we use the approximation
# atanh(z) ~ 1/z +/- i*pi/2 (+/- depending on the sign
# of y
h = math.hypot(x/2., y/2.) # safe from overflow
real = x/4./h/h
# the two negations in the next line cancel each other out
# except when working with unsigned zeros: they're there to
# ensure that the branch cut has the correct continuity on
# systems that don't support signed zeros
imag = -copysign(math.pi/2., -y)
elif x == 1. and ay < CM_SQRT_DBL_MIN:
# C99 standard says: atanh(1+/-0.) should be inf +/- 0i
if ay == 0.:
raise ValueError("math domain error")
#real = INF
#imag = y
else:
real = -math.log(math.sqrt(ay)/math.sqrt(math.hypot(ay, 2.)))
imag = copysign(math.atan2(2., -ay) / 2, y)
else:
real = log1p(4.*x/((1-x)*(1-x) + ay*ay))/4.
imag = -math.atan2(-2.*y, (1-x)*(1+x) - ay*ay) / 2.
return (real, imag)
def __eq__(self, other):
if (type(self) is SomeFloat and type(other) is SomeFloat and
self.is_constant() and other.is_constant()):
from pypy.rlib.rfloat import isnan, copysign
# NaN unpleasantness.
if isnan(self.const) and isnan(other.const):
return True
# 0.0 vs -0.0 unpleasantness.
if not self.const and not other.const:
return copysign(1., self.const) == copysign(1., other.const)
#
return super(SomeFloat, self).__eq__(other)
def c_sqrt(x, y):
# Method: use symmetries to reduce to the case when x = z.real and y
# = z.imag are nonnegative. Then the real part of the result is
# given by
#
# s = sqrt((x + hypot(x, y))/2)
#
# and the imaginary part is
#
# d = (y/2)/s
#
# If either x or y is very large then there's a risk of overflow in
# computation of the expression x + hypot(x, y). We can avoid this
# by rewriting the formula for s as:
#
# s = 2*sqrt(x/8 + hypot(x/8, y/8))
#
# This costs us two extra multiplications/divisions, but avoids the
# overhead of checking for x and y large.
#
# If both x and y are subnormal then hypot(x, y) may also be
# subnormal, so will lack full precision. We solve this by rescaling
# x and y by a sufficiently large power of 2 to ensure that x and y
# are normal.
if not isfinite(x) or not isfinite(y):
return sqrt_special_values[special_type(x)][special_type(y)]
if x == 0. and y == 0.:
return (0., y)
ax = fabs(x)
ay = fabs(y)
if ax < DBL_MIN and ay < DBL_MIN and (ax > 0. or ay > 0.):
# here we catch cases where hypot(ax, ay) is subnormal
ax = math.ldexp(ax, CM_SCALE_UP)
ay1= math.ldexp(ay, CM_SCALE_UP)
s = math.ldexp(math.sqrt(ax + math.hypot(ax, ay1)),
CM_SCALE_DOWN)
else:
ax /= 8.
s = 2.*math.sqrt(ax + math.hypot(ax, ay/8.))
d = ay/(2.*s)
if x >= 0.:
return (s, copysign(d, y))
else:
return (d, copysign(s, y))
def rAssertAlmostEqual(a, b, rel_err = 2e-15, abs_err = 5e-323, msg=''):
"""Fail if the two floating-point numbers are not almost equal.
Determine whether floating-point values a and b are equal to within
a (small) rounding error. The default values for rel_err and
abs_err are chosen to be suitable for platforms where a float is
represented by an IEEE 754 double. They allow an error of between
9 and 19 ulps.
"""
# special values testing
if isnan(a):
if isnan(b):
return
raise AssertionError(msg + '%r should be nan' % (b,))
if isinf(a):
if a == b:
return
raise AssertionError(msg + 'finite result where infinity expected: '
'expected %r, got %r' % (a, b))
# if both a and b are zero, check whether they have the same sign
# (in theory there are examples where it would be legitimate for a
# and b to have opposite signs; in practice these hardly ever
# occur).
if not a and not b:
# only check it if we are running on top of CPython >= 2.6
if sys.version_info >= (2, 6) and copysign(1., a) != copysign(1., b):
raise AssertionError(msg + 'zero has wrong sign: expected %r, '
'got %r' % (a, b))
# if a-b overflows, or b is infinite, return False. Again, in
# theory there are examples where a is within a few ulps of the
# max representable float, and then b could legitimately be
# infinite. In practice these examples are rare.
try:
absolute_error = abs(b-a)
except OverflowError:
pass
else:
# test passes if either the absolute error or the relative
# error is sufficiently small. The defaults amount to an
# error of between 9 ulps and 19 ulps on an IEEE-754 compliant
# machine.
if absolute_error <= max(abs_err, rel_err * abs(a)):
return
raise AssertionError(msg + '%r and %r are not sufficiently close' % (a, b))
def rAssertAlmostEqual(a, b, rel_err=2e-15, abs_err=5e-323, msg=''):
"""Fail if the two floating-point numbers are not almost equal.
Determine whether floating-point values a and b are equal to within
a (small) rounding error. The default values for rel_err and
abs_err are chosen to be suitable for platforms where a float is
represented by an IEEE 754 double. They allow an error of between
9 and 19 ulps.
"""
# special values testing
if isnan(a):
if isnan(b):
return
raise AssertionError(msg + '%r should be nan' % (b, ))
if isinf(a):
if a == b:
return
raise AssertionError(msg + 'finite result where infinity expected: '
'expected %r, got %r' % (a, b))
# if both a and b are zero, check whether they have the same sign
# (in theory there are examples where it would be legitimate for a
# and b to have opposite signs; in practice these hardly ever
# occur).
if not a and not b:
# only check it if we are running on top of CPython >= 2.6
if sys.version_info >= (2, 6) and copysign(1., a) != copysign(1., b):
raise AssertionError(msg + 'zero has wrong sign: expected %r, '
'got %r' % (a, b))
# if a-b overflows, or b is infinite, return False. Again, in
# theory there are examples where a is within a few ulps of the
# max representable float, and then b could legitimately be
# infinite. In practice these examples are rare.
try:
absolute_error = abs(b - a)
except OverflowError:
pass
else:
# test passes if either the absolute error or the relative
# error is sufficiently small. The defaults amount to an
# error of between 9 ulps and 19 ulps on an IEEE-754 compliant
# machine.
if absolute_error <= max(abs_err, rel_err * abs(a)):
return
raise AssertionError(msg + '%r and %r are not sufficiently close' % (a, b))
def float_hex__Float(space, w_float):
value = w_float.floatval
if not isfinite(value):
return str__Float(space, w_float)
if value == 0.0:
if copysign(1., value) == -1.:
return space.wrap("-0x0.0p+0")
else:
return space.wrap("0x0.0p+0")
mant, exp = math.frexp(value)
shift = 1 - max(rfloat.DBL_MIN_EXP - exp, 0)
mant = math.ldexp(mant, shift)
mant = abs(mant)
exp -= shift
result = ['\0'] * ((TOHEX_NBITS - 1) // 4 + 2)
result[0] = _char_from_hex(int(mant))
mant -= int(mant)
result[1] = "."
for i in range((TOHEX_NBITS - 1) // 4):
mant *= 16.0
result[i + 2] = _char_from_hex(int(mant))
mant -= int(mant)
if exp < 0:
sign = "-"
else:
sign = "+"
exp = abs(exp)
s = ''.join(result)
if value < 0.0:
return space.wrap("-0x%sp%s%d" % (s, sign, exp))
else:
return space.wrap("0x%sp%s%d" % (s, sign, exp))
def div(self, v1, v2):
try:
return v1 / v2
except ZeroDivisionError:
if v1 == v2 == 0.0:
return rfloat.NAN
return rfloat.copysign(rfloat.INFINITY, v1 * v2)
def div(self, v1, v2):
# XXX this won't work after translation, probably requires ovfcheck
try:
return v1 / v2
except ZeroDivisionError:
if v1 == v2 == 0.0:
return rfloat.NAN
return rfloat.copysign(rfloat.INFINITY, v1 * v2)
def test_special_values():
from pypy.module.cmath.special_value import sqrt_special_values
assert len(sqrt_special_values) == 7
assert len(sqrt_special_values[4]) == 7
assert isinstance(sqrt_special_values[5][1], tuple)
assert sqrt_special_values[5][1][0] == 1e200 * 1e200
assert sqrt_special_values[5][1][1] == -0.
assert copysign(1., sqrt_special_values[5][1][1]) == -1.
def test_special_values():
from pypy.module.cmath.special_value import sqrt_special_values
assert len(sqrt_special_values) == 7
assert len(sqrt_special_values[4]) == 7
assert isinstance(sqrt_special_values[5][1], tuple)
assert sqrt_special_values[5][1][0] == 1e200 * 1e200
assert sqrt_special_values[5][1][1] == -0.
assert copysign(1., sqrt_special_values[5][1][1]) == -1.
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 pow(self, v1, v2):
try:
return math.pow(v1, v2)
except ValueError:
return rfloat.NAN
except OverflowError:
if math.modf(v2)[0] == 0 and math.modf(v2 / 2)[0] != 0:
# Odd integer powers result in the same sign as the base
return rfloat.copysign(rfloat.INFINITY, v1)
return rfloat.INFINITY
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)
def c_tanh(x, y):
# Formula:
#
# tanh(x+iy) = (tanh(x)(1+tan(y)^2) + i tan(y)(1-tanh(x))^2) /
# (1+tan(y)^2 tanh(x)^2)
#
# To avoid excessive roundoff error, 1-tanh(x)^2 is better computed
# as 1/cosh(x)^2. When abs(x) is large, we approximate 1-tanh(x)^2
# by 4 exp(-2*x) instead, to avoid possible overflow in the
# computation of cosh(x).
if not isfinite(x) or not isfinite(y):
if isinf(x) and isfinite(y) and y != 0.:
if x > 0:
real = 1.0 # vv XXX why is the 2. there?
imag = copysign(0., 2. * math.sin(y) * math.cos(y))
else:
real = -1.0
imag = copysign(0., 2. * math.sin(y) * math.cos(y))
r = (real, imag)
else:
r = tanh_special_values[special_type(x)][special_type(y)]
# need to raise ValueError if y is +/-infinity and x is finite
if isinf(y) and isfinite(x):
raise ValueError("math domain error")
return r
if fabs(x) > CM_LOG_LARGE_DOUBLE:
real = copysign(1., x)
imag = 4. * math.sin(y) * math.cos(y) * math.exp(-2.*fabs(x))
else:
tx = math.tanh(x)
ty = math.tan(y)
cx = 1. / math.cosh(x)
txty = tx * ty
denom = 1. + txty * txty
real = tx * (1. + ty*ty) / denom
imag = ((ty / denom) * cx) * cx
return real, imag
def _make_key(self, obj):
# see the tests 'test_zeros_not_mixed*' in ../test/test_compiler.py
space = self.space
w_type = space.type(obj)
if space.is_w(w_type, space.w_float):
val = space.float_w(obj)
if val == 0.0 and rfloat.copysign(1., val) < 0:
w_key = space.newtuple([obj, space.w_float, space.w_None])
else:
w_key = space.newtuple([obj, space.w_float])
elif space.is_w(w_type, space.w_complex):
w_real = space.getattr(obj, space.wrap("real"))
w_imag = space.getattr(obj, space.wrap("imag"))
real = space.float_w(w_real)
imag = space.float_w(w_imag)
real_negzero = (real == 0.0 and
rfloat.copysign(1., real) < 0)
imag_negzero = (imag == 0.0 and
rfloat.copysign(1., imag) < 0)
if real_negzero and imag_negzero:
tup = [obj, space.w_complex, space.w_None, space.w_None,
space.w_None]
elif imag_negzero:
tup = [obj, space.w_complex, space.w_None, space.w_None]
elif real_negzero:
tup = [obj, space.w_complex, space.w_None]
else:
tup = [obj, space.w_complex]
w_key = space.newtuple(tup)
elif space.is_w(w_type, space.w_tuple):
result_w = [obj, w_type]
for w_item in space.fixedview(obj):
result_w.append(self._make_key(w_item))
w_key = space.newtuple(result_w[:])
else:
w_key = space.newtuple([obj, w_type])
return w_key
def _sinpi(x):
y = math.fmod(abs(x), 2.)
n = int(rfloat.round_away(2. * y))
if n == 0:
r = math.sin(math.pi * y)
elif n == 1:
r = math.cos(math.pi * (y - .5))
elif n == 2:
r = math.sin(math.pi * (1. - y))
elif n == 3:
r = -math.cos(math.pi * (y - 1.5))
elif n == 4:
r = math.sin(math.pi * (y - 2.))
else:
raise AssertionError("should not reach")
return rfloat.copysign(1., x) * r
def _sinpi(x):
y = math.fmod(abs(x), 2.)
n = int(rfloat.round_away(2. * y))
if n == 0:
r = math.sin(math.pi * y)
elif n == 1:
r = math.cos(math.pi * (y - .5))
elif n == 2:
r = math.sin(math.pi * (1. - y))
elif n == 3:
r = -math.cos(math.pi * (y - 1.5))
elif n == 4:
r = math.sin(math.pi * (y - 2.))
else:
raise AssertionError("should not reach")
return rfloat.copysign(1., x) * r
def __init__(self, value):
self.value = value # a concrete value
# try to be smart about constant mutable or immutable values
key = type(self.value), self.value # to avoid confusing e.g. 0 and 0.0
#
# we also have to avoid confusing 0.0 and -0.0 (needed e.g. for
# translating the cmath module)
if key[0] is float and not self.value:
from pypy.rlib.rfloat import copysign
if copysign(1., self.value) == -1.: # -0.0
key = (float, "-0.0")
#
try:
hash(key)
except TypeError:
key = id(self.value)
self.key = key
def special_type(d):
if isnan(d):
return ST_NAN
elif isinf(d):
if d > 0.0:
return ST_PINF
else:
return ST_NINF
else:
if d != 0.0:
if d > 0.0:
return ST_POS
else:
return ST_NEG
else:
if copysign(1., d) == 1.:
return ST_PZERO
else:
return ST_NZERO
def mod__Float_Float(space, w_float1, w_float2):
x = w_float1.floatval
y = w_float2.floatval
if y == 0.0:
raise FailedToImplementArgs(space.w_ZeroDivisionError, space.wrap("float modulo"))
try:
mod = math.fmod(x, y)
except ValueError:
mod = rfloat.NAN
else:
if mod:
# ensure the remainder has the same sign as the denominator
if (y < 0.0) != (mod < 0.0):
mod += y
else:
# the remainder is zero, and in the presence of signed zeroes
# fmod returns different results across platforms; ensure
# it has the same sign as the denominator; we'd like to do
# "mod = y * 0.0", but that may get optimized away
mod = copysign(0.0, y)
return W_FloatObject(mod)
def c_phase(x, y):
# Windows screws up atan2 for inf and nan, and alpha Tru64 5.1 doesn't
# follow C99 for atan2(0., 0.).
if isnan(x) or isnan(y):
return NAN
if isinf(y):
if isinf(x):
if copysign(1., x) == 1.:
# atan2(+-inf, +inf) == +-pi/4
return copysign(0.25 * math.pi, y)
else:
# atan2(+-inf, -inf) == +-pi*3/4
return copysign(0.75 * math.pi, y)
# atan2(+-inf, x) == +-pi/2 for finite x
return copysign(0.5 * math.pi, y)
if isinf(x) or y == 0.:
if copysign(1., x) == 1.:
# atan2(+-y, +inf) = atan2(+-0, +x) = +-0.
return copysign(0., y)
else:
# atan2(+-y, -inf) = atan2(+-0., -x) = +-pi.
return copysign(math.pi, y)
return math.atan2(y, x)
def sign(value):
if value == 0.0:
return 0.0
return rfloat.copysign(1.0, value)
def _format_complex(self, w_complex):
space = self.space
tp = self._type
self._get_locale(tp)
default_precision = 6
if self._align == "=":
# '=' alignment is invalid
msg = ("'=' alignment flag is not allowed in"
" complex format specifier")
raise OperationError(space.w_ValueError, space.wrap(msg))
if self._fill_char == "0":
#zero padding is invalid
msg = "Zero padding is not allowed in complex format specifier"
raise OperationError(space.w_ValueError, space.wrap(msg))
if self._alternate:
#alternate is invalid
msg = "Alternate form %s not allowed in complex format specifier"
raise OperationError(space.w_ValueError,
space.wrap(msg % (self._alternate)))
skip_re = 0
add_parens = 0
if tp == "\0":
#should mirror str() output
tp = "g"
default_precision = 12
#test if real part is non-zero
if (w_complex.realval == 0 and
copysign(1., w_complex.realval) == 1.):
skip_re = 1
else:
add_parens = 1
if tp == "n":
#same as 'g' except for locale, taken care of later
tp = "g"
#check if precision not set
if self._precision == -1:
self._precision = default_precision
#might want to switch to double_to_string from formatd
#in CPython it's named 're' - clashes with re module
re_num = formatd(w_complex.realval, tp, self._precision)
im_num = formatd(w_complex.imagval, tp, self._precision)
n_re_digits = len(re_num)
n_im_digits = len(im_num)
to_real_number = 0
to_imag_number = 0
re_sign = im_sign = ''
#if a sign character is in the output, remember it and skip
if re_num[0] == "-":
re_sign = "-"
to_real_number = 1
n_re_digits -= 1
if im_num[0] == "-":
im_sign = "-"
to_imag_number = 1
n_im_digits -= 1
#turn off padding - do it after number composition
#calc_num_width uses self._width, so assign to temporary variable,
#calculate width of real and imag parts, then reassign padding, align
tmp_fill_char = self._fill_char
tmp_align = self._align
tmp_width = self._width
self._fill_char = "\0"
self._align = "<"
self._width = -1
#determine if we have remainder, might include dec or exponent or both
re_have_dec, re_remainder_ptr = self._parse_number(re_num,
to_real_number)
im_have_dec, im_remainder_ptr = self._parse_number(im_num,
to_imag_number)
if self.is_unicode:
re_num = re_num.decode("ascii")
im_num = im_num.decode("ascii")
#set remainder, in CPython _parse_number sets this
#using n_re_digits causes tests to fail
re_n_remainder = len(re_num) - re_remainder_ptr
im_n_remainder = len(im_num) - im_remainder_ptr
re_spec = self._calc_num_width(0, re_sign, to_real_number, n_re_digits,
re_n_remainder, re_have_dec,
re_num)
#capture grouped digits b/c _fill_number reads from self._grouped_digits
#self._grouped_digits will get overwritten in imaginary calc_num_width
re_grouped_digits = self._grouped_digits
if not skip_re:
self._sign = "+"
im_spec = self._calc_num_width(0, im_sign, to_imag_number, n_im_digits,
im_n_remainder, im_have_dec,
im_num)
im_grouped_digits = self._grouped_digits
if skip_re:
re_spec.n_total = 0
#reassign width, alignment, fill character
self._align = tmp_align
self._width = tmp_width
self._fill_char = tmp_fill_char
#compute L and R padding - stored in self._left_pad and self._right_pad
self._calc_padding(self.empty, re_spec.n_total + im_spec.n_total + 1 +
add_parens * 2)
out = self._builder()
fill = self._fill_char
if fill == "\0":
fill = self._lit(" ")[0]
#compose the string
#add left padding
out.append_multiple_char(fill, self._left_pad)
if add_parens:
out.append(self._lit('(')[0])
#if the no. has a real component, add it
if not skip_re:
out.append(self._fill_number(re_spec, re_num, to_real_number, 0,
fill, re_remainder_ptr, False,
re_grouped_digits))
#add imaginary component
out.append(self._fill_number(im_spec, im_num, to_imag_number, 0,
fill, im_remainder_ptr, False,
im_grouped_digits))
#add 'j' character
out.append(self._lit('j')[0])
if add_parens:
out.append(self._lit(')')[0])
#add right padding
out.append_multiple_char(fill, self._right_pad)
return self.space.wrap(out.build())
def pow__Float_Float_ANY(space, w_float1, w_float2, thirdArg):
# This raises FailedToImplement in cases like overflow where a
# (purely theoretical) big-precision float implementation would have
# a chance to give a result, and directly OperationError for errors
# that we want to force to be reported to the user.
if not space.is_w(thirdArg, space.w_None):
raise OperationError(space.w_TypeError, space.wrap(
"pow() 3rd argument not allowed unless all arguments are integers"))
x = w_float1.floatval
y = w_float2.floatval
# Sort out special cases here instead of relying on pow()
if y == 0.0:
# x**0 is 1, even 0**0
return W_FloatObject(1.0)
if isnan(x):
# nan**y = nan, unless y == 0
return W_FloatObject(x)
if isnan(y):
# x**nan = nan, unless x == 1; x**nan = x
if x == 1.0:
return W_FloatObject(1.0)
else:
return W_FloatObject(y)
if isinf(y):
# x**inf is: 0.0 if abs(x) < 1; 1.0 if abs(x) == 1; inf if
# abs(x) > 1 (including case where x infinite)
#
# x**-inf is: inf if abs(x) < 1; 1.0 if abs(x) == 1; 0.0 if
# abs(x) > 1 (including case where v infinite)
x = abs(x)
if x == 1.0:
return W_FloatObject(1.0)
elif (y > 0.0) == (x > 1.0):
return W_FloatObject(INFINITY)
else:
return W_FloatObject(0.0)
if isinf(x):
# (+-inf)**w is: inf for w positive, 0 for w negative; in oth
# cases, we need to add the appropriate sign if w is an odd
# integer.
y_is_odd = math.fmod(abs(y), 2.0) == 1.0
if y > 0.0:
if y_is_odd:
return W_FloatObject(x)
else:
return W_FloatObject(abs(x))
else:
if y_is_odd:
return W_FloatObject(copysign(0.0, x))
else:
return W_FloatObject(0.0)
if x == 0.0:
if y < 0.0:
raise OperationError(space.w_ZeroDivisionError,
space.wrap("0.0 cannot be raised to "
"a negative power"))
negate_result = False
# special case: "(-1.0) ** bignum" should not raise ValueError,
# unlike "math.pow(-1.0, bignum)". See http://mail.python.org/
# - pipermail/python-bugs-list/2003-March/016795.html
if x < 0.0:
if isnan(y):
return W_FloatObject(NAN)
if math.floor(y) != y:
raise OperationError(space.w_ValueError,
space.wrap("negative number cannot be "
"raised to a fractional power"))
# y is an exact integer, albeit perhaps a very large one.
# Replace x by its absolute value and remember to negate the
# pow result if y is odd.
x = -x
negate_result = math.fmod(abs(y), 2.0) == 1.0
if x == 1.0:
# (-1) ** large_integer also ends up here
if negate_result:
return W_FloatObject(-1.0)
else:
return W_FloatObject(1.0)
try:
# We delegate to our implementation of math.pow() the error detection.
z = math.pow(x,y)
except OverflowError:
raise FailedToImplementArgs(space.w_OverflowError,
space.wrap("float power"))
except ValueError:
raise OperationError(space.w_ValueError,
space.wrap("float power"))
if negate_result:
z = -z
return W_FloatObject(z)
def reciprocal(self, v):
if v == 0.0:
return rfloat.copysign(rfloat.INFINITY, v)
return 1.0 / v
def sign(self, v):
if v == 0.0:
return 0.0
return rfloat.copysign(1.0, v)
def signbit(self, v):
return rfloat.copysign(1.0, v) < 0.0