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authorDavid Cournapeau <cournape@gmail.com>2009-09-16 07:14:48 +0000
committerDavid Cournapeau <cournape@gmail.com>2009-09-16 07:14:48 +0000
commit064d50496ce946cb54e0901ac10967d9e0126b20 (patch)
tree84b41e7e95bf4b9b34a0da92fa9133665e50d48e /numpy/lib/machar.py
parent1c321def2841860d97cd335a6a34fc8abed4a548 (diff)
downloadnumpy-064d50496ce946cb54e0901ac10967d9e0126b20.tar.gz
Move finfo into core.
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diff --git a/numpy/lib/machar.py b/numpy/lib/machar.py
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-"""
-Machine arithmetics - determine the parameters of the
-floating-point arithmetic system
-"""
-# Author: Pearu Peterson, September 2003
-
-
-__all__ = ['MachAr']
-
-from numpy.core.fromnumeric import any
-from numpy.core.numeric import seterr
-
-# Need to speed this up...especially for longfloat
-
-class MachAr(object):
- """
- Diagnosing machine parameters.
-
- Attributes
- ----------
- ibeta : int
- Radix in which numbers are represented.
- it : int
- Number of base-`ibeta` digits in the floating point mantissa M.
- machep : int
- Exponent of the smallest (most negative) power of `ibeta` that,
- added to 1.0, gives something different from 1.0
- eps : float
- Floating-point number ``beta**machep`` (floating point precision)
- negep : int
- Exponent of the smallest power of `ibeta` that, substracted
- from 1.0, gives something different from 1.0.
- epsneg : float
- Floating-point number ``beta**negep``.
- iexp : int
- Number of bits in the exponent (including its sign and bias).
- minexp : int
- Smallest (most negative) power of `ibeta` consistent with there
- being no leading zeros in the mantissa.
- xmin : float
- Floating point number ``beta**minexp`` (the smallest [in
- magnitude] usable floating value).
- maxexp : int
- Smallest (positive) power of `ibeta` that causes overflow.
- xmax : float
- ``(1-epsneg) * beta**maxexp`` (the largest [in magnitude]
- usable floating value).
- irnd : int
- In ``range(6)``, information on what kind of rounding is done
- in addition, and on how underflow is handled.
- ngrd : int
- Number of 'guard digits' used when truncating the product
- of two mantissas to fit the representation.
-
- epsilon : float
- Same as `eps`.
- tiny : float
- Same as `xmin`.
- huge : float
- Same as `xmax`.
- precision : float
- ``- int(-log10(eps))``
- resolution : float
- `` - 10**(-precision)``
-
- References
- ----------
- .. [1] Press, Teukolsky, Vetterling and Flannery,
- "Numerical Recipes in C++," 2nd ed,
- Cambridge University Press, 2002, p. 31.
-
- """
- def __init__(self, float_conv=float,int_conv=int,
- float_to_float=float,
- float_to_str = lambda v:'%24.16e' % v,
- title = 'Python floating point number'):
- """
- float_conv - convert integer to float (array)
- int_conv - convert float (array) to integer
- float_to_float - convert float array to float
- float_to_str - convert array float to str
- title - description of used floating point numbers
- """
- # We ignore all errors here because we are purposely triggering
- # underflow to detect the properties of the runninng arch.
- saverrstate = seterr(under='ignore')
- try:
- self._do_init(float_conv, int_conv, float_to_float, float_to_str, title)
- finally:
- seterr(**saverrstate)
-
- 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)
-
- def __str__(self):
- return '''\
-Machine parameters for %(title)s
----------------------------------------------------------------------
-ibeta=%(ibeta)s it=%(it)s iexp=%(iexp)s ngrd=%(ngrd)s irnd=%(irnd)s
-machep=%(machep)s eps=%(_str_eps)s (beta**machep == epsilon)
-negep =%(negep)s epsneg=%(_str_epsneg)s (beta**epsneg)
-minexp=%(minexp)s xmin=%(_str_xmin)s (beta**minexp == tiny)
-maxexp=%(maxexp)s xmax=%(_str_xmax)s ((1-epsneg)*beta**maxexp == huge)
----------------------------------------------------------------------
-''' % self.__dict__
-
-
-if __name__ == '__main__':
- print MachAr()