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Machine arithmetic - determine the parameters of the
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floating-point arithmetic system
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Author: Pearu Peterson, September 2003
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Diagnosing machine parameters.
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Attributes
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----------
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ibeta : int
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Radix in which numbers are represented.
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it : int
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Number of base-`ibeta` digits in the floating point mantissa M.
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machep : int
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Exponent of the smallest (most negative) power of `ibeta` that,
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added to 1.0, gives something different from 1.0
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eps : float
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Floating-point number ``beta**machep`` (floating point precision)
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negep : int
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Exponent of the smallest power of `ibeta` that, subtracted
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from 1.0, gives something different from 1.0.
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epsneg : float
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Floating-point number ``beta**negep``.
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iexp : int
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Number of bits in the exponent (including its sign and bias).
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minexp : int
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Smallest (most negative) power of `ibeta` consistent with there
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being no leading zeros in the mantissa.
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xmin : float
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Floating-point number ``beta**minexp`` (the smallest [in
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magnitude] positive floating point number with full precision).
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maxexp : int
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Smallest (positive) power of `ibeta` that causes overflow.
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xmax : float
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``(1-epsneg) * beta**maxexp`` (the largest [in magnitude]
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usable floating value).
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irnd : int
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In ``range(6)``, information on what kind of rounding is done
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in addition, and on how underflow is handled.
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ngrd : int
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Number of 'guard digits' used when truncating the product
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of two mantissas to fit the representation.
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epsilon : float
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Same as `eps`.
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tiny : float
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An alias for `smallest_normal`, kept for backwards compatibility.
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huge : float
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Same as `xmax`.
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precision : float
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``- int(-log10(eps))``
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resolution : float
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``- 10**(-precision)``
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smallest_normal : float
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The smallest positive floating point number with 1 as leading bit in
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the mantissa following IEEE-754. Same as `xmin`.
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smallest_subnormal : float
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The smallest positive floating point number with 0 as leading bit in
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the mantissa following IEEE-754.
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Parameters
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----------
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float_conv : function, optional
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Function that converts an integer or integer array to a float
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or float array. Default is `float`.
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int_conv : function, optional
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Function that converts a float or float array to an integer or
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integer array. Default is `int`.
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float_to_float : function, optional
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Function that converts a float array to float. Default is `float`.
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Note that this does not seem to do anything useful in the current
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implementation.
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float_to_str : function, optional
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Function that converts a single float to a string. Default is
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``lambda v:'%24.16e' %v``.
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title : str, optional
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Title that is printed in the string representation of `MachAr`.
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See Also
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--------
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finfo : Machine limits for floating point types.
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iinfo : Machine limits for integer types.
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References
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----------
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.. [1] Press, Teukolsky, Vetterling and Flannery,
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"Numerical Recipes in C++," 2nd ed,
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Cambridge University Press, 2002, p. 31.
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float_conv - convert integer to float (array)
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int_conv - convert float (array) to integer
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float_to_float - convert float array to float
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float_to_str - convert array float to str
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title - description of used floating point numbers
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zMachAr._do_initc C s d}|| j S )NaC Machine parameters for %(title)s
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---------------------------------------------------------------------
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ibeta=%(ibeta)s it=%(it)s iexp=%(iexp)s ngrd=%(ngrd)s irnd=%(irnd)s
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machep=%(machep)s eps=%(_str_eps)s (beta**machep == epsilon)
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negep =%(negep)s epsneg=%(_str_epsneg)s (beta**epsneg)
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minexp=%(minexp)s xmin=%(_str_xmin)s (beta**minexp == tiny)
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maxexp=%(maxexp)s xmax=%(_str_xmax)s ((1-epsneg)*beta**maxexp == huge)
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smallest_normal=%(smallest_normal)s smallest_subnormal=%(smallest_subnormal)s
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---------------------------------------------------------------------
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