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Machine arithmetic - determine the parameters of the
floating-point arithmetic system
Author: Pearu Peterson, September 2003
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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, subtracted
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] positive floating point number with full precision).
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
An alias for `smallest_normal`, kept for backwards compatibility.
huge : float
Same as `xmax`.
precision : float
``- int(-log10(eps))``
resolution : float
``- 10**(-precision)``
smallest_normal : float
The smallest positive floating point number with 1 as leading bit in
the mantissa following IEEE-754. Same as `xmin`.
smallest_subnormal : float
The smallest positive floating point number with 0 as leading bit in
the mantissa following IEEE-754.
Parameters
----------
float_conv : function, optional
Function that converts an integer or integer array to a float
or float array. Default is `float`.
int_conv : function, optional
Function that converts a float or float array to an integer or
integer array. Default is `int`.
float_to_float : function, optional
Function that converts a float array to float. Default is `float`.
Note that this does not seem to do anything useful in the current
implementation.
float_to_str : function, optional
Function that converts a single float to a string. Default is
``lambda v:'%24.16e' %v``.
title : str, optional
Title that is printed in the string representation of `MachAr`.
See Also
--------
finfo : Machine limits for floating point types.
iinfo : Machine limits for integer types.
References
----------
.. [1] Press, Teukolsky, Vetterling and Flannery,
"Numerical Recipes in C++," 2nd ed,
Cambridge University Press, 2002, p. 31.
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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)
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maxexp=%(maxexp)s xmax=%(_str_xmax)s ((1-epsneg)*beta**maxexp == huge)
smallest_normal=%(smallest_normal)s smallest_subnormal=%(smallest_subnormal)s
---------------------------------------------------------------------
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