def _do_init(self, float_conv, int_conv, float_to_float, float_to_str,
title):
max_iterN = 10000
msg = "Did not converge after %d tries with %s"
one = float_conv(1)
two = one + one
zero = one - one
# Do we really need to do this? Aren't they 2 and 2.0?
# Determine ibeta and beta
a = one
for _ in range(max_iterN):
a = a + a
temp = a + one
temp1 = temp - a
if any(temp1 - one != zero):
break
else:
raise RuntimeError(msg % (_, one.dtype))
b = one
for _ in range(max_iterN):
b = b + b
temp = a + b
itemp = int_conv(temp - a)
if any(itemp != 0):
break
else:
raise RuntimeError(msg % (_, one.dtype))
ibeta = itemp
beta = float_conv(ibeta)
# Determine it and irnd
it = -1
b = one
for _ in range(max_iterN):
it = it + 1
b = b * beta
temp = b + one
temp1 = temp - b
if any(temp1 - one != zero):
break
else:
raise RuntimeError(msg % (_, one.dtype))
betah = beta / two
a = one
for _ in range(max_iterN):
a = a + a
temp = a + one
temp1 = temp - a
if any(temp1 - one != zero):
break
else:
raise RuntimeError(msg % (_, one.dtype))
temp = a + betah
irnd = 0
if any(temp - a != zero):
irnd = 1
tempa = a + beta
temp = tempa + betah
if irnd == 0 and any(temp - tempa != zero):
irnd = 2
# Determine negep and epsneg
negep = it + 3
betain = one / beta
a = one
for i in range(negep):
a = a * betain
b = a
for _ in range(max_iterN):
temp = one - a
if any(temp - one != zero):
break
a = a * beta
negep = negep - 1
# Prevent infinite loop on PPC with gcc 4.0:
if negep < 0:
raise RuntimeError("could not determine machine tolerance "
"for 'negep', locals() -> %s" % (locals()))
else:
raise RuntimeError(msg % (_, one.dtype))
negep = -negep
epsneg = a
# Determine machep and eps
machep = -it - 3
a = b
for _ in range(max_iterN):
temp = one + a
if any(temp - one != zero):
break
a = a * beta
machep = machep + 1
else:
raise RuntimeError(msg % (_, one.dtype))
eps = a
# Determine ngrd
ngrd = 0
temp = one + eps
if irnd == 0 and any(temp * one - one != zero):
ngrd = 1
# Determine iexp
i = 0
k = 1
z = betain
t = one + eps
nxres = 0
for _ in range(max_iterN):
y = z
z = y * y
a = z * one # Check here for underflow
temp = z * t
if any(a + a == zero) or any(abs(z) >= y):
break
temp1 = temp * betain
if any(temp1 * beta == z):
break
i = i + 1
k = k + k
else:
raise RuntimeError(msg % (_, one.dtype))
if ibeta != 10:
iexp = i + 1
mx = k + k
else:
iexp = 2
iz = ibeta
while k >= iz:
iz = iz * ibeta
iexp = iexp + 1
mx = iz + iz - 1
# Determine minexp and xmin
for _ in range(max_iterN):
xmin = y
y = y * betain
a = y * one
temp = y * t
if any((a + a) != zero) and any(abs(y) < xmin):
k = k + 1
temp1 = temp * betain
if any(temp1 * beta == y) and any(temp != y):
nxres = 3
xmin = y
break
else:
break
else:
raise RuntimeError(msg % (_, one.dtype))
minexp = -k
# Determine maxexp, xmax
if mx <= k + k - 3 and ibeta != 10:
mx = mx + mx
iexp = iexp + 1
maxexp = mx + minexp
irnd = irnd + nxres
if irnd >= 2:
maxexp = maxexp - 2
i = maxexp + minexp
if ibeta == 2 and not i:
maxexp = maxexp - 1
if i > 20:
maxexp = maxexp - 1
if any(a != y):
maxexp = maxexp - 2
xmax = one - epsneg
if any(xmax * one != xmax):
xmax = one - beta * epsneg
xmax = xmax / (xmin * beta * beta * beta)
i = maxexp + minexp + 3
for j in range(i):
if ibeta == 2:
xmax = xmax + xmax
else:
xmax = xmax * beta
smallest_subnormal = abs(xmin / beta**(it))
self.ibeta = ibeta
self.it = it
self.negep = negep
self.epsneg = float_to_float(epsneg)
self._str_epsneg = float_to_str(epsneg)
self.machep = machep
self.eps = float_to_float(eps)
self._str_eps = float_to_str(eps)
self.ngrd = ngrd
self.iexp = iexp
self.minexp = minexp
self.xmin = float_to_float(xmin)
self._str_xmin = float_to_str(xmin)
self.maxexp = maxexp
self.xmax = float_to_float(xmax)
self._str_xmax = float_to_str(xmax)
self.irnd = irnd
self.title = title
# Commonly used parameters
self.epsilon = self.eps
self.tiny = self.xmin
self.huge = self.xmax
self.smallest_normal = self.xmin
self.smallest_subnormal = float_to_float(smallest_subnormal)
import math
self.precision = int(-math.log10(float_to_float(self.eps)))
ten = two + two + two + two + two
resolution = ten**(-self.precision)
self.resolution = float_to_float(resolution)
self._str_resolution = float_to_str(resolution)
def _do_init(self, float_conv, int_conv, float_to_float, float_to_str, title):
max_iterN = 10000
msg = "Did not converge after %d tries with %s"
one = float_conv(1)
two = one + one
zero = one - one
# Do we really need to do this? Aren't they 2 and 2.0?
# Determine ibeta and beta
a = one
for _ in xrange(max_iterN):
a = a + a
temp = a + one
temp1 = temp - a
if any(temp1 - one != zero):
break
else:
raise RuntimeError(msg % (_, one.dtype))
b = one
for _ in xrange(max_iterN):
b = b + b
temp = a + b
itemp = int_conv(temp-a)
if any(itemp != 0):
break
else:
raise RuntimeError(msg % (_, one.dtype))
ibeta = itemp
beta = float_conv(ibeta)
# Determine it and irnd
it = -1
b = one
for _ in xrange(max_iterN):
it = it + 1
b = b * beta
temp = b + one
temp1 = temp - b
if any(temp1 - one != zero):
break
else:
raise RuntimeError(msg % (_, one.dtype))
betah = beta / two
a = one
for _ in xrange(max_iterN):
a = a + a
temp = a + one
temp1 = temp - a
if any(temp1 - one != zero):
break
else:
raise RuntimeError(msg % (_, one.dtype))
temp = a + betah
irnd = 0
if any(temp-a != zero):
irnd = 1
tempa = a + beta
temp = tempa + betah
if irnd==0 and any(temp-tempa != zero):
irnd = 2
# Determine negep and epsneg
negep = it + 3
betain = one / beta
a = one
for i in range(negep):
a = a * betain
b = a
for _ in xrange(max_iterN):
temp = one - a
if any(temp-one != zero):
break
a = a * beta
negep = negep - 1
# Prevent infinite loop on PPC with gcc 4.0:
if negep < 0:
raise RuntimeError("could not determine machine tolerance "
"for 'negep', locals() -> %s" % (locals()))
else:
raise RuntimeError(msg % (_, one.dtype))
negep = -negep
epsneg = a
# Determine machep and eps
machep = - it - 3
a = b
for _ in xrange(max_iterN):
temp = one + a
if any(temp-one != zero):
break
a = a * beta
machep = machep + 1
else:
raise RuntimeError(msg % (_, one.dtype))
eps = a
# Determine ngrd
ngrd = 0
temp = one + eps
if irnd==0 and any(temp*one - one != zero):
ngrd = 1
# Determine iexp
i = 0
k = 1
z = betain
t = one + eps
nxres = 0
for _ in xrange(max_iterN):
y = z
z = y*y
a = z*one # Check here for underflow
temp = z*t
if any(a+a == zero) or any(abs(z)>=y):
break
temp1 = temp * betain
if any(temp1*beta == z):
break
i = i + 1
k = k + k
else:
raise RuntimeError(msg % (_, one.dtype))
if ibeta != 10:
iexp = i + 1
mx = k + k
else:
iexp = 2
iz = ibeta
while k >= iz:
iz = iz * ibeta
iexp = iexp + 1
mx = iz + iz - 1
# Determine minexp and xmin
for _ in xrange(max_iterN):
xmin = y
y = y * betain
a = y * one
temp = y * t
if any(a+a != zero) and any(abs(y) < xmin):
k = k + 1
temp1 = temp * betain
if any(temp1*beta == y) and any(temp != y):
nxres = 3
xmin = y
break
else:
break
else:
raise RuntimeError(msg % (_, one.dtype))
minexp = -k
# Determine maxexp, xmax
if mx <= k + k - 3 and ibeta != 10:
mx = mx + mx
iexp = iexp + 1
maxexp = mx + minexp
irnd = irnd + nxres
if irnd >= 2:
maxexp = maxexp - 2
i = maxexp + minexp
if ibeta == 2 and not i:
maxexp = maxexp - 1
if i > 20:
maxexp = maxexp - 1
if any(a != y):
maxexp = maxexp - 2
xmax = one - epsneg
if any(xmax*one != xmax):
xmax = one - beta*epsneg
xmax = xmax / (xmin*beta*beta*beta)
i = maxexp + minexp + 3
for j in range(i):
if ibeta==2:
xmax = xmax + xmax
else:
xmax = xmax * beta
self.ibeta = ibeta
self.it = it
self.negep = negep
self.epsneg = float_to_float(epsneg)
self._str_epsneg = float_to_str(epsneg)
self.machep = machep
self.eps = float_to_float(eps)
self._str_eps = float_to_str(eps)
self.ngrd = ngrd
self.iexp = iexp
self.minexp = minexp
self.xmin = float_to_float(xmin)
self._str_xmin = float_to_str(xmin)
self.maxexp = maxexp
self.xmax = float_to_float(xmax)
self._str_xmax = float_to_str(xmax)
self.irnd = irnd
self.title = title
# Commonly used parameters
self.epsilon = self.eps
self.tiny = self.xmin
self.huge = self.xmax
import math
self.precision = int(-math.log10(float_to_float(self.eps)))
ten = two + two + two + two + two
resolution = ten ** (-self.precision)
self.resolution = float_to_float(resolution)
self._str_resolution = float_to_str(resolution)
