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Machine arithmetics - determine the parameters of the
floating-point arithmetic system

Author: Pearu Peterson, September 2003

�MachAr�)�any)�errstate)�
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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
        Same as `xmin`.
    huge : float
        Same as `xmax`.
    precision : float
        ``- int(-log10(eps))``
    resolution : float
        ``- 10**(-precision)``

    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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        title        - description of used floating point numbers

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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)
minexp=%(minexp)s   xmin=%(_str_xmin)s (beta**minexp == tiny)
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