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_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 test_math_sqrt(self):
def f(x):
try:
return math.sqrt(x)
except ValueError:
return -INFINITY
res = self.interp_operations(f, [0.0])
assert res == 0.0
self.check_operations_history(call_pure=1)
#
res = self.interp_operations(f, [25.0])
assert res == 5.0
self.check_operations_history(call_pure=1)
#
res = self.interp_operations(f, [-0.0])
assert str(res) == '-0.0'
self.check_operations_history(call_pure=1)
#
res = self.interp_operations(f, [1000000.0])
assert res == 1000.0
self.check_operations_history(call_pure=1)
#
res = self.interp_operations(f, [-1.0])
assert res == -INFINITY
self.check_operations_history(call_pure=0)
#
res = self.interp_operations(f, [INFINITY])
assert isinf(res) and not isnan(res) and res > 0.0
self.check_operations_history(call_pure=0)
#
res = self.interp_operations(f, [NAN])
assert isnan(res) and not isinf(res)
self.check_operations_history(call_pure=0)
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 round(space, number, w_ndigits=0):
"""round(number[, ndigits]) -> floating point number
Round a number to a given precision in decimal digits (default 0 digits).
This always returns a floating point number. Precision may be negative."""
# Algorithm copied directly from CPython
# interpret 2nd argument as a Py_ssize_t; clip on overflow
ndigits = space.getindex_w(w_ndigits, None)
# nans, infinities and zeros round to themselves
if number == 0 or isinf(number) or isnan(number):
return space.wrap(number)
# Deal with extreme values for ndigits. For ndigits > NDIGITS_MAX, x
# always rounds to itself. For ndigits < NDIGITS_MIN, x always
# rounds to +-0.0.
if ndigits > NDIGITS_MAX:
return space.wrap(number)
elif ndigits < NDIGITS_MIN:
# return 0.0, but with sign of x
return space.wrap(0.0 * number)
# finite x, and ndigits is not unreasonably large
z = round_double(number, ndigits)
if isinf(z):
raise OperationError(space.w_OverflowError, space.wrap("rounded value too large to represent"))
return space.wrap(z)
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 ll_math_atan2(y, x):
"""wrapper for atan2 that deals directly with special cases before
delegating to the platform libm for the remaining cases. This
is necessary to get consistent behaviour across platforms.
Windows, FreeBSD and alpha Tru64 are amongst platforms that don't
always follow C99.
"""
if isnan(x) or isnan(y):
return NAN
if isinf(y):
if isinf(x):
if math_copysign(1.0, x) == 1.0:
# atan2(+-inf, +inf) == +-pi/4
return math_copysign(0.25 * math.pi, y)
else:
# atan2(+-inf, -inf) == +-pi*3/4
return math_copysign(0.75 * math.pi, y)
# atan2(+-inf, x) == +-pi/2 for finite x
return math_copysign(0.5 * math.pi, y)
if isinf(x) or y == 0.0:
if math_copysign(1.0, x) == 1.0:
# atan2(+-y, +inf) = atan2(+-0, +x) = +-0.
return math_copysign(0.0, y)
else:
# atan2(+-y, -inf) = atan2(+-0., -x) = +-pi.
return math_copysign(math.pi, y)
return math_atan2(y, x)
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 round(space, number, w_ndigits=0):
"""round(number[, ndigits]) -> floating point number
Round a number to a given precision in decimal digits (default 0 digits).
This always returns a floating point number. Precision may be negative."""
# Algorithm copied directly from CPython
# interpret 2nd argument as a Py_ssize_t; clip on overflow
ndigits = space.getindex_w(w_ndigits, None)
# nans, infinities and zeros round to themselves
if number == 0 or isinf(number) or isnan(number):
return space.wrap(number)
# Deal with extreme values for ndigits. For ndigits > NDIGITS_MAX, x
# always rounds to itself. For ndigits < NDIGITS_MIN, x always
# rounds to +-0.0.
if ndigits > NDIGITS_MAX:
return space.wrap(number)
elif ndigits < NDIGITS_MIN:
# return 0.0, but with sign of x
return space.wrap(0.0 * number)
# finite x, and ndigits is not unreasonably large
z = round_double(number, ndigits)
if isinf(z):
raise OperationError(
space.w_OverflowError,
space.wrap("rounded value too large to represent"))
return space.wrap(z)
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 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 ll_math_atan2(y, x):
"""wrapper for atan2 that deals directly with special cases before
delegating to the platform libm for the remaining cases. This
is necessary to get consistent behaviour across platforms.
Windows, FreeBSD and alpha Tru64 are amongst platforms that don't
always follow C99.
"""
if isnan(x):
return NAN
if not isfinite(y):
if isnan(y):
return NAN
if isinf(x):
if math_copysign(1.0, x) == 1.0:
# atan2(+-inf, +inf) == +-pi/4
return math_copysign(0.25 * math.pi, y)
else:
# atan2(+-inf, -inf) == +-pi*3/4
return math_copysign(0.75 * math.pi, y)
# atan2(+-inf, x) == +-pi/2 for finite x
return math_copysign(0.5 * math.pi, y)
if isinf(x) or y == 0.0:
if math_copysign(1.0, x) == 1.0:
# atan2(+-y, +inf) = atan2(+-0, +x) = +-0.
return math_copysign(0.0, y)
else:
# atan2(+-y, -inf) = atan2(+-0., -x) = +-pi.
return math_copysign(math.pi, y)
return math_atan2(y, x)
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 ll_math_pow(x, y):
# deal directly with IEEE specials, to cope with problems on various
# platforms whose semantics don't exactly match C99
if isnan(y):
if x == 1.0:
return 1.0 # 1**Nan = 1
return y
if not isfinite(x):
if isnan(x):
if y == 0.0:
return 1.0 # NaN**0 = 1
return x
else: # isinf(x)
odd_y = not isinf(y) and math_fmod(math_fabs(y), 2.0) == 1.0
if y > 0.0:
if odd_y:
return x
return math_fabs(x)
elif y == 0.0:
return 1.0
else: # y < 0.0
if odd_y:
return math_copysign(0.0, x)
return 0.0
if isinf(y):
if math_fabs(x) == 1.0:
return 1.0
elif y > 0.0 and math_fabs(x) > 1.0:
return y
elif y < 0.0 and math_fabs(x) < 1.0:
if x == 0.0:
raise ValueError("0**-inf: divide by zero")
return -y # result is +inf
else:
return 0.0
_error_reset()
r = math_pow(x, y)
errno = rposix.get_errno()
if not isfinite(r):
if isnan(r):
# a NaN result should arise only from (-ve)**(finite non-integer)
errno = EDOM
else: # isinf(r)
# an infinite result here arises either from:
# (A) (+/-0.)**negative (-> divide-by-zero)
# (B) overflow of x**y with x and y finite
if x == 0.0:
errno = EDOM
else:
errno = ERANGE
if errno:
_likely_raise(errno, r)
return r
def ll_math_pow(x, y):
# deal directly with IEEE specials, to cope with problems on various
# platforms whose semantics don't exactly match C99
if isnan(y):
if x == 1.0:
return 1.0 # 1**Nan = 1
return y
if not isfinite(x):
if isnan(x):
if y == 0.0:
return 1.0 # NaN**0 = 1
return x
else: # isinf(x)
odd_y = not isinf(y) and math_fmod(math_fabs(y), 2.0) == 1.0
if y > 0.0:
if odd_y:
return x
return math_fabs(x)
elif y == 0.0:
return 1.0
else: # y < 0.0
if odd_y:
return math_copysign(0.0, x)
return 0.0
if isinf(y):
if math_fabs(x) == 1.0:
return 1.0
elif y > 0.0 and math_fabs(x) > 1.0:
return y
elif y < 0.0 and math_fabs(x) < 1.0:
if x == 0.0:
raise ValueError("0**-inf: divide by zero")
return -y # result is +inf
else:
return 0.0
_error_reset()
r = math_pow(x, y)
errno = rposix.get_errno()
if not isfinite(r):
if isnan(r):
# a NaN result should arise only from (-ve)**(finite non-integer)
errno = EDOM
else: # isinf(r)
# an infinite result here arises either from:
# (A) (+/-0.)**negative (-> divide-by-zero)
# (B) overflow of x**y with x and y finite
if x == 0.0:
errno = EDOM
else:
errno = ERANGE
if errno:
_likely_raise(errno, r)
return r
def _gamma(x):
if rfloat.isnan(x) or (rfloat.isinf(x) and x > 0.):
return x
if rfloat.isinf(x):
raise ValueError("math domain error")
if x == 0.:
raise ValueError("math domain error")
if x == math.floor(x):
if x < 0.:
raise ValueError("math domain error")
if x < len(_gamma_integrals):
return _gamma_integrals[int(x) - 1]
absx = abs(x)
if absx < 1e-20:
r = 1. / x
if rfloat.isinf(r):
raise OverflowError("math range error")
return r
if absx > 200.:
if x < 0.:
return 0. / -_sinpi(x)
else:
raise OverflowError("math range error")
y = absx + _lanczos_g_minus_half
if absx > _lanczos_g_minus_half:
q = y - absx
z = q - _lanczos_g_minus_half
else:
q = y - _lanczos_g_minus_half
z = q - absx
z = z * _lanczos_g / y
if x < 0.:
r = -math.pi / _sinpi(absx) / absx * math.exp(y) / _lanczos_sum(absx)
r -= z * r
if absx < 140.:
r /= math.pow(y, absx - .5)
else:
sqrtpow = math.pow(y, absx / 2. - .25)
r /= sqrtpow
r /= sqrtpow
else:
r = _lanczos_sum(absx) / math.exp(y)
r += z * r
if absx < 140.:
r *= math.pow(y, absx - .5)
else:
sqrtpow = math.pow(y, absx / 2. - .25)
r *= sqrtpow
r *= sqrtpow
if rfloat.isinf(r):
raise OverflowError("math range error")
return r
def _gamma(x):
if rfloat.isnan(x) or (rfloat.isinf(x) and x > 0.):
return x
if rfloat.isinf(x):
raise ValueError("math domain error")
if x == 0.:
raise ValueError("math domain error")
if x == math.floor(x):
if x < 0.:
raise ValueError("math domain error")
if x < len(_gamma_integrals):
return _gamma_integrals[int(x) - 1]
absx = abs(x)
if absx < 1e-20:
r = 1. / x
if rfloat.isinf(r):
raise OverflowError("math range error")
return r
if absx > 200.:
if x < 0.:
return 0. / -_sinpi(x)
else:
raise OverflowError("math range error")
y = absx + _lanczos_g_minus_half
if absx > _lanczos_g_minus_half:
q = y - absx
z = q - _lanczos_g_minus_half
else:
q = y - _lanczos_g_minus_half
z = q - absx
z = z * _lanczos_g / y
if x < 0.:
r = -math.pi / _sinpi(absx) / absx * math.exp(y) / _lanczos_sum(absx)
r -= z * r
if absx < 140.:
r /= math.pow(y, absx - .5)
else:
sqrtpow = math.pow(y, absx / 2. - .25)
r /= sqrtpow
r /= sqrtpow
else:
r = _lanczos_sum(absx) / math.exp(y)
r += z * r
if absx < 140.:
r *= math.pow(y, absx - .5)
else:
sqrtpow = math.pow(y, absx / 2. - .25)
r *= sqrtpow
r *= sqrtpow
if rfloat.isinf(r):
raise OverflowError("math range error")
return r
def push_primitive_constant(self, TYPE, value):
ilasm = self.ilasm
if TYPE is ootype.Void:
pass
elif TYPE is ootype.Bool:
ilasm.opcode('ldc.i4', str(int(value)))
elif TYPE is ootype.Char or TYPE is ootype.UniChar:
ilasm.opcode('ldc.i4', ord(value))
elif TYPE is ootype.Float:
if isinf(value):
if value < 0.0:
ilasm.opcode('ldc.r8', '(00 00 00 00 00 00 f0 ff)')
else:
ilasm.opcode('ldc.r8', '(00 00 00 00 00 00 f0 7f)')
elif isnan(value):
ilasm.opcode('ldc.r8', '(00 00 00 00 00 00 f8 ff)')
else:
ilasm.opcode('ldc.r8', repr(value))
elif isinstance(value, CDefinedIntSymbolic):
ilasm.opcode('ldc.i4', DEFINED_INT_SYMBOLICS[value.expr])
elif TYPE in (ootype.Signed, ootype.Unsigned, rffi.SHORT):
ilasm.opcode('ldc.i4', str(value))
elif TYPE in (ootype.SignedLongLong, ootype.UnsignedLongLong):
ilasm.opcode('ldc.i8', str(value))
elif TYPE in (ootype.String, ootype.Unicode):
if value._str is None:
ilasm.opcode('ldnull')
else:
ilasm.opcode("ldstr", string_literal(value._str))
else:
assert False, "Unexpected constant type"
def push_primitive_constant(self, TYPE, value):
ilasm = self.ilasm
if TYPE is ootype.Void:
pass
elif TYPE is ootype.Bool:
ilasm.opcode("ldc.i4", str(int(value)))
elif TYPE is ootype.Char or TYPE is ootype.UniChar:
ilasm.opcode("ldc.i4", ord(value))
elif TYPE is ootype.Float:
if isinf(value):
if value < 0.0:
ilasm.opcode("ldc.r8", "(00 00 00 00 00 00 f0 ff)")
else:
ilasm.opcode("ldc.r8", "(00 00 00 00 00 00 f0 7f)")
elif isnan(value):
ilasm.opcode("ldc.r8", "(00 00 00 00 00 00 f8 ff)")
else:
ilasm.opcode("ldc.r8", repr(value))
elif isinstance(value, CDefinedIntSymbolic):
ilasm.opcode("ldc.i4", DEFINED_INT_SYMBOLICS[value.expr])
elif TYPE in (ootype.Signed, ootype.Unsigned, rffi.SHORT):
ilasm.opcode("ldc.i4", str(value))
elif TYPE in (ootype.SignedLongLong, ootype.UnsignedLongLong):
ilasm.opcode("ldc.i8", str(value))
elif TYPE in (ootype.String, ootype.Unicode):
if value._str is None:
ilasm.opcode("ldnull")
else:
ilasm.opcode("ldstr", string_literal(value._str))
else:
assert False, "Unexpected constant type"
def format_float(self, w_value, char):
space = self.space
x = space.float_w(maybe_float(space, w_value))
if isnan(x):
if char in 'EFG':
r = 'NAN'
else:
r = 'nan'
elif isinf(x):
if x < 0:
if char in 'EFG':
r = '-INF'
else:
r = '-inf'
else:
if char in 'EFG':
r = 'INF'
else:
r = 'inf'
else:
prec = self.prec
if prec < 0:
prec = 6
if char in 'fF' and x / 1e25 > 1e25:
char = chr(ord(char) + 1) # 'f' => 'g'
flags = 0
if self.f_alt:
flags |= DTSF_ALT
r = formatd(x, char, prec, flags)
self.std_wp_number(r)
def format_float(self, w_value, char):
space = self.space
x = space.float_w(maybe_float(space, w_value))
if isnan(x):
if char in 'EFG':
r = 'NAN'
else:
r = 'nan'
elif isinf(x):
if x < 0:
if char in 'EFG':
r = '-INF'
else:
r = '-inf'
else:
if char in 'EFG':
r = 'INF'
else:
r = 'inf'
else:
prec = self.prec
if prec < 0:
prec = 6
if char in 'fF' and x/1e25 > 1e25:
char = chr(ord(char) + 1) # 'f' => 'g'
flags = 0
if self.f_alt:
flags |= DTSF_ALT
r = formatd(x, char, prec, flags)
self.std_wp_number(r)
def c_abs(x, y):
if not isfinite(x) or not isfinite(y):
# C99 rules: if either the real or the imaginary part is an
# infinity, return infinity, even if the other part is a NaN.
if isinf(x):
return INF
if isinf(y):
return INF
# either the real or imaginary part is a NaN,
# and neither is infinite. Result should be NaN.
return NAN
result = math.hypot(x, y)
if not isfinite(result):
raise OverflowError("math range error")
return result
def isfinitejs(ctx, args, this):
if len(args) < 1:
return newbool(True)
n = args[0].ToNumber(ctx)
if isinf(n) or isnan(n):
return newbool(False)
else:
return newbool(True)
def ll_math_fmod(x, y):
if isinf(x) and not isnan(y):
raise ValueError("math domain error")
if y == 0:
raise ValueError("math domain error")
return math_fmod(x, y)
def ll_math_fmod(x, y):
if isinf(y):
if isinf(x):
raise ValueError("math domain error")
return x # fmod(x, +/-Inf) returns x for finite x (or if x is a NaN).
_error_reset()
r = math_fmod(x, y)
errno = rposix.get_errno()
if isnan(r):
if isnan(x) or isnan(y):
errno = 0
else:
errno = EDOM
if errno:
_likely_raise(errno, r)
return r
def c_abs(x, y):
if not isfinite(x) or not isfinite(y):
# C99 rules: if either the real or the imaginary part is an
# infinity, return infinity, even if the other part is a NaN.
if isinf(x):
return INF
if isinf(y):
return INF
# either the real or imaginary part is a NaN,
# and neither is infinite. Result should be NaN.
return NAN
result = math.hypot(x, y)
if not isfinite(result):
raise OverflowError("math range error")
return result
def format_float(x, code, precision):
# like float2string, except that the ".0" is not necessary
if isinf(x):
if x > 0.0:
return "inf"
else:
return "-inf"
elif isnan(x):
return "nan"
else:
return formatd(x, code, precision)
def format_float(x, code, precision):
# like float2string, except that the ".0" is not necessary
if isinf(x):
if x > 0.0:
return "inf"
else:
return "-inf"
elif isnan(x):
return "nan"
else:
return formatd(x, code, precision)
def ll_math(x):
_error_reset()
r = c_func(x)
# Error checking fun. Copied from CPython 2.6
errno = rposix.get_errno()
if isnan(r):
if isnan(x):
errno = 0
else:
errno = EDOM
elif isinf(r):
if isinf(x) or isnan(x):
errno = 0
elif can_overflow:
errno = ERANGE
else:
errno = EDOM
if errno:
_likely_raise(errno, r)
return r
def ll_math_ldexp(x, exp):
if x == 0.0 or isinf(x) or isnan(x):
return x # NaNs, zeros and infinities are returned unchanged
if exp > INT_MAX:
# overflow (64-bit platforms only)
r = math_copysign(INFINITY, x)
errno = ERANGE
elif exp < INT_MIN:
# underflow to +-0 (64-bit platforms only)
r = math_copysign(0.0, x)
errno = 0
else:
_error_reset()
r = math_ldexp(x, exp)
errno = rposix.get_errno()
if isinf(r):
errno = ERANGE
if errno:
_likely_raise(errno, r)
return r
def name_float(value, db):
if isinf(value):
if value > 0:
return '(Py_HUGE_VAL)'
else:
return '(-Py_HUGE_VAL)'
elif isnan(value):
return '(Py_HUGE_VAL/Py_HUGE_VAL)'
else:
x = repr(value)
assert not x.startswith('n')
return x
def name_singlefloat(value, db):
value = float(value)
if isinf(value):
if value > 0:
return '((float)Py_HUGE_VAL)'
else:
return '((float)-Py_HUGE_VAL)'
elif isnan(value):
# XXX are these expressions ok?
return '((float)(Py_HUGE_VAL/Py_HUGE_VAL))'
else:
return repr(value) + 'f'
def float2string(x, code, precision):
# we special-case explicitly inf and nan here
if isfinite(x):
s = formatd(x, code, precision, DTSF_ADD_DOT_0)
elif isinf(x):
if x > 0.0:
s = "inf"
else:
s = "-inf"
else: # isnan(x):
s = "nan"
return s
def name_singlefloat(value, db):
value = float(value)
if isinf(value):
if value > 0:
return '((float)Py_HUGE_VAL)'
else:
return '((float)-Py_HUGE_VAL)'
elif isnan(value):
# XXX are these expressions ok?
return '((float)(Py_HUGE_VAL/Py_HUGE_VAL))'
else:
return repr(value) + 'f'
def name_float(value, db):
if isinf(value):
if value > 0:
return '(Py_HUGE_VAL)'
else:
return '(-Py_HUGE_VAL)'
elif isnan(value):
return '(Py_HUGE_VAL/Py_HUGE_VAL)'
else:
x = repr(value)
assert not x.startswith('n')
return x
def float2string(x, code, precision):
# we special-case explicitly inf and nan here
if isfinite(x):
s = formatd(x, code, precision, DTSF_ADD_DOT_0)
elif isinf(x):
if x > 0.0:
s = "inf"
else:
s = "-inf"
else: # isnan(x):
s = "nan"
return s
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_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 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 _lgamma(x):
if rfloat.isnan(x):
return x
if rfloat.isinf(x):
return rfloat.INFINITY
if x == math.floor(x) and x <= 2.:
if x <= 0.:
raise ValueError("math range error")
return 0.
absx = abs(x)
if absx < 1e-20:
return -math.log(absx)
if x > 0.:
r = (math.log(_lanczos_sum(x)) - _lanczos_g + (x - .5) *
(math.log(x + _lanczos_g - .5) - 1))
else:
r = (math.log(math.pi) - math.log(abs(_sinpi(absx))) - math.log(absx) -
(math.log(_lanczos_sum(absx)) - _lanczos_g + (absx - .5) *
(math.log(absx + _lanczos_g - .5) - 1)))
if rfloat.isinf(r):
raise OverflowError("math domain error")
return r
def _push_double_constant(self, value):
if isnan(value):
jvm.DOUBLENAN.load(self)
elif isinf(value):
if value > 0: jvm.DOUBLEPOSINF.load(self)
else: jvm.DOUBLENEGINF.load(self)
elif value == 0.0:
self.emit(jvm.DCONST_0)
elif value == 1.0:
self.emit(jvm.DCONST_1)
else:
# Big hack to avoid exponential notation:
self.emit(jvm.LDC2, "%22.22f" % value)
def ll_math_frexp(x):
# deal with special cases directly, to sidestep platform differences
if isnan(x) or isinf(x) or not x:
mantissa = x
exponent = 0
else:
exp_p = lltype.malloc(rffi.INTP.TO, 1, flavor='raw')
try:
mantissa = math_frexp(x, exp_p)
exponent = rffi.cast(lltype.Signed, exp_p[0])
finally:
lltype.free(exp_p, flavor='raw')
return (mantissa, exponent)
def _lgamma(x):
if rfloat.isnan(x):
return x
if rfloat.isinf(x):
return rfloat.INFINITY
if x == math.floor(x) and x <= 2.:
if x <= 0.:
raise ValueError("math range error")
return 0.
absx = abs(x)
if absx < 1e-20:
return -math.log(absx)
if x > 0.:
r = (math.log(_lanczos_sum(x)) - _lanczos_g + (x - .5) *
(math.log(x + _lanczos_g - .5) - 1))
else:
r = (math.log(math.pi) - math.log(abs(_sinpi(absx))) - math.log(absx) -
(math.log(_lanczos_sum(absx)) - _lanczos_g +
(absx - .5) * (math.log(absx + _lanczos_g - .5) - 1)))
if rfloat.isinf(r):
raise OverflowError("math domain error")
return r
def fsum(space, w_iterable):
"""Sum an iterable of floats, trying to keep precision."""
w_iter = space.iter(w_iterable)
inf_sum = special_sum = 0.0
partials = []
while True:
try:
w_value = space.next(w_iter)
except OperationError, e:
if not e.match(space, space.w_StopIteration):
raise
break
v = _get_double(space, w_value)
original = v
added = 0
for y in partials:
if abs(v) < abs(y):
v, y = y, v
hi = v + y
yr = hi - v
lo = y - yr
if lo != 0.0:
partials[added] = lo
added += 1
v = hi
del partials[added:]
if v != 0.0:
if rfloat.isinf(v) or rfloat.isnan(v):
if (not rfloat.isinf(original) and
not rfloat.isnan(original)):
raise OperationError(space.w_OverflowError,
space.wrap("intermediate overflow"))
if rfloat.isinf(original):
inf_sum += original
special_sum += original
del partials[:]
else:
partials.append(v)
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 ll_math_hypot(x, y):
# hypot(x, +/-Inf) returns Inf, even if x is a NaN.
if isinf(x):
return math_fabs(x)
if isinf(y):
return math_fabs(y)
_error_reset()
r = math_hypot(x, y)
errno = rposix.get_errno()
if isnan(r):
if isnan(x) or isnan(y):
errno = 0
else:
errno = EDOM
elif isinf(r):
if isinf(x) or isnan(x) or isinf(y) or isnan(y):
errno = 0
else:
errno = ERANGE
if errno:
_likely_raise(errno, r)
return r
def ll_math_modf(x):
# some platforms don't do the right thing for NaNs and
# infinities, so we take care of special cases directly.
if isinf(x):
return (math_copysign(0.0, x), x)
elif isnan(x):
return (x, x)
intpart_p = lltype.malloc(rffi.DOUBLEP.TO, 1, flavor='raw')
try:
fracpart = math_modf(x, intpart_p)
intpart = intpart_p[0]
finally:
lltype.free(intpart_p, flavor='raw')
return (fracpart, intpart)
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 fsum(space, w_iterable):
"""Sum an iterable of floats, trying to keep precision."""
w_iter = space.iter(w_iterable)
inf_sum = special_sum = 0.0
partials = []
while True:
try:
w_value = space.next(w_iter)
except OperationError, e:
if not e.match(space, space.w_StopIteration):
raise
break
v = _get_double(space, w_value)
original = v
added = 0
for y in partials:
if abs(v) < abs(y):
v, y = y, v
hi = v + y
yr = hi - v
lo = y - yr
if lo != 0.0:
partials[added] = lo
added += 1
v = hi
del partials[added:]
if v != 0.0:
if rfloat.isinf(v) or rfloat.isnan(v):
if (not rfloat.isinf(original) and not rfloat.isnan(original)):
raise OperationError(space.w_OverflowError,
space.wrap("intermediate overflow"))
if rfloat.isinf(original):
inf_sum += original
special_sum += original
del partials[:]
else:
partials.append(v)
def ll_math_hypot(x, y):
# hypot(x, +/-Inf) returns Inf, even if x is a NaN.
if isinf(x):
return math_fabs(x)
if isinf(y):
return math_fabs(y)
_error_reset()
r = math_hypot(x, y)
errno = rposix.get_errno()
if not isfinite(r):
if isnan(r):
if isnan(x) or isnan(y):
errno = 0
else:
errno = EDOM
else: # isinf(r)
if isfinite(x) and isfinite(y):
errno = ERANGE
else:
errno = 0
if errno:
_likely_raise(errno, r)
return r
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 ll_math_fmod(x, y):
# fmod(x, +/-Inf) returns x for finite x.
if isinf(y) and isfinite(x):
return x
_error_reset()
r = math_fmod(x, y)
errno = rposix.get_errno()
if isnan(r):
if isnan(x) or isnan(y):
errno = 0
else:
errno = EDOM
if errno:
_likely_raise(errno, r)
return r
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 ll_math_ldexp(x, exp):
if x == 0.0 or not isfinite(x):
return x # NaNs, zeros and infinities are returned unchanged
if exp > INT_MAX:
# overflow (64-bit platforms only)
r = math_copysign(INFINITY, x)
errno = ERANGE
elif exp < INT_MIN:
# underflow to +-0 (64-bit platforms only)
r = math_copysign(0.0, x)
errno = 0
else:
_error_reset()
r = math_ldexp(x, exp)
errno = rposix.get_errno()
if isinf(r):
errno = ERANGE
if errno:
_likely_raise(errno, r)
return r
def _hash_float(f):
"""The algorithm behind compute_hash() for a float.
This implementation is identical to the CPython implementation,
except the fact that the integer case is not treated specially.
In RPython, floats cannot be used with ints in dicts, anyway.
"""
from pypy.rlib.rarithmetic import intmask
from pypy.rlib.rfloat import isfinite, isinf
if not isfinite(f):
if isinf(f):
if f < 0.0:
return -271828
else:
return 314159
else: #isnan(f):
return 0
v, expo = math.frexp(f)
v *= TAKE_NEXT
hipart = int(v)
v = (v - float(hipart)) * TAKE_NEXT
x = hipart + int(v) + (expo << 15)
return intmask(x)
def float_as_integer_ratio__Float(space, w_float):
value = w_float.floatval
if isinf(value):
w_msg = space.wrap("cannot pass infinity to as_integer_ratio()")
raise OperationError(space.w_OverflowError, w_msg)
elif isnan(value):
w_msg = space.wrap("cannot pass nan to as_integer_ratio()")
raise OperationError(space.w_ValueError, w_msg)
float_part, exp = math.frexp(value)
for i in range(300):
if float_part == math.floor(float_part):
break
float_part *= 2.0
exp -= 1
w_num = W_LongObject.fromfloat(space, float_part)
w_den = space.newlong(1)
w_exp = space.newlong(abs(exp))
w_exp = space.lshift(w_den, w_exp)
if exp > 0:
w_num = space.mul(w_num, w_exp)
else:
w_den = w_exp
# Try to return int.
return space.newtuple([space.int(w_num), space.int(w_den)])
def ll_math_cos(x):
if isinf(x):
raise ValueError("math domain error")
return math_cos(x)