def logaddexp(self, v1, v2):
tmp = v1 - v2
if tmp > 0:
return v1 + rfloat.log1p(math.exp(-tmp))
elif tmp <= 0:
return v2 + rfloat.log1p(math.exp(tmp))
else:
return v1 + v2
def logaddexp(self, v1, v2):
tmp = v1 - v2
if tmp > 0:
return v1 + rfloat.log1p(math.exp(-tmp))
elif tmp <= 0:
return v2 + rfloat.log1p(math.exp(tmp))
else:
return v1 + v2
def log1p(self, v):
try:
return rfloat.log1p(v)
except OverflowError:
return -rfloat.INFINITY
except ValueError:
return rfloat.NAN
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 log1p(self, v):
try:
return rfloat.log1p(v)
except OverflowError:
return -rfloat.INFINITY
except ValueError:
return rfloat.NAN
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_log(x, y):
# The usual formula for the real part is log(hypot(z.real, z.imag)).
# There are four situations where this formula is potentially
# problematic:
#
# (1) the absolute value of z is subnormal. Then hypot is subnormal,
# so has fewer than the usual number of bits of accuracy, hence may
# have large relative error. This then gives a large absolute error
# in the log. This can be solved by rescaling z by a suitable power
# of 2.
#
# (2) the absolute value of z is greater than DBL_MAX (e.g. when both
# z.real and z.imag are within a factor of 1/sqrt(2) of DBL_MAX)
# Again, rescaling solves this.
#
# (3) the absolute value of z is close to 1. In this case it's
# difficult to achieve good accuracy, at least in part because a
# change of 1ulp in the real or imaginary part of z can result in a
# change of billions of ulps in the correctly rounded answer.
#
# (4) z = 0. The simplest thing to do here is to call the
# floating-point log with an argument of 0, and let its behaviour
# (returning -infinity, signaling a floating-point exception, setting
# errno, or whatever) determine that of c_log. So the usual formula
# is fine here.
# XXX the following two lines seem unnecessary at least on Linux;
# the tests pass fine without them
if not isfinite(x) or not isfinite(y):
return log_special_values[special_type(x)][special_type(y)]
ax = fabs(x)
ay = fabs(y)
if ax > CM_LARGE_DOUBLE or ay > CM_LARGE_DOUBLE:
real = math.log(math.hypot(ax / 2., ay / 2.)) + M_LN2
elif ax < DBL_MIN and ay < DBL_MIN:
if ax > 0. or ay > 0.:
# catch cases where hypot(ax, ay) is subnormal
real = math.log(
math.hypot(math.ldexp(ax, DBL_MANT_DIG),
math.ldexp(ay, DBL_MANT_DIG)))
real -= DBL_MANT_DIG * M_LN2
else:
# log(+/-0. +/- 0i)
raise ValueError("math domain error")
#real = -INF
#imag = atan2(y, x)
else:
h = math.hypot(ax, ay)
if 0.71 <= h and h <= 1.73:
am = max(ax, ay)
an = min(ax, ay)
real = log1p((am - 1) * (am + 1) + an * an) / 2.
else:
real = math.log(h)
imag = math.atan2(y, x)
return (real, imag)
def c_log(x, y):
# The usual formula for the real part is log(hypot(z.real, z.imag)).
# There are four situations where this formula is potentially
# problematic:
#
# (1) the absolute value of z is subnormal. Then hypot is subnormal,
# so has fewer than the usual number of bits of accuracy, hence may
# have large relative error. This then gives a large absolute error
# in the log. This can be solved by rescaling z by a suitable power
# of 2.
#
# (2) the absolute value of z is greater than DBL_MAX (e.g. when both
# z.real and z.imag are within a factor of 1/sqrt(2) of DBL_MAX)
# Again, rescaling solves this.
#
# (3) the absolute value of z is close to 1. In this case it's
# difficult to achieve good accuracy, at least in part because a
# change of 1ulp in the real or imaginary part of z can result in a
# change of billions of ulps in the correctly rounded answer.
#
# (4) z = 0. The simplest thing to do here is to call the
# floating-point log with an argument of 0, and let its behaviour
# (returning -infinity, signaling a floating-point exception, setting
# errno, or whatever) determine that of c_log. So the usual formula
# is fine here.
# XXX the following two lines seem unnecessary at least on Linux;
# the tests pass fine without them
if not isfinite(x) or not isfinite(y):
return log_special_values[special_type(x)][special_type(y)]
ax = fabs(x)
ay = fabs(y)
if ax > CM_LARGE_DOUBLE or ay > CM_LARGE_DOUBLE:
real = math.log(math.hypot(ax/2., ay/2.)) + M_LN2
elif ax < DBL_MIN and ay < DBL_MIN:
if ax > 0. or ay > 0.:
# catch cases where hypot(ax, ay) is subnormal
real = math.log(math.hypot(math.ldexp(ax, DBL_MANT_DIG),
math.ldexp(ay, DBL_MANT_DIG)))
real -= DBL_MANT_DIG*M_LN2
else:
# log(+/-0. +/- 0i)
raise ValueError("math domain error")
#real = -INF
#imag = atan2(y, x)
else:
h = math.hypot(ax, ay)
if 0.71 <= h and h <= 1.73:
am = max(ax, ay)
an = min(ax, ay)
real = log1p((am-1)*(am+1) + an*an) / 2.
else:
real = math.log(h)
imag = math.atan2(y, x)
return (real, imag)
def npy_log2_1p(self, v):
return log2e * rfloat.log1p(v)
def npy_log2_1p(self, v):
return log2e * rfloat.log1p(v)
