Extra functions on the built-in `float` similar to those on `Decimal`.

# floatextras Extra functions on the built-in float similar to those on Decimal.

## API

>>> from floatextras import * >>> f = -123.456 >>> as_tuple(f) FloatTuple(sign=1, digits=(1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1), exponent=6) >>> sign, digits, exponent = as_tuple(f) >>> from_tuple((0, digits, exponent+1)) 246.912 >>> next_minus(f) -123.45600000000002 >>> next_plus(f) -123.45599999999999 >>> next_toward(f, 0) -123.45599999999999 >>> float_difference(1, next_minus(next_minus(1))) 2 >>> qnan2 = make_nan(2) >>> isnan(qnan2) True >>> isqnan(qnan2) True >>> issnan(qnan2) False >>> nan_payload(qnan2) 2 >>> isqnan(float('nan')) True >>> nan_payload(float('nan')) 0

The functions as_tuple, next_minus, next_plus, and next_toward have the same effect as the corresponding methods on [Decimal][1] objects, but for values of the builtin [float][2] type, and from_tuple is equivalent to the Decimal constructor from a tuple.

[1]: https://docs.python.org/3/library/decimal.html [2]: https://docs.python.org/3/library/stdtypes.html#numeric-types-int-float-complex

The float_difference function is an inverse next_plus–it tells you how many times you’d need to call next_plus on g to get f.

The nan functions are utility functions to construct and examine NaN values with specific payloads.

An optional direct argument to most functions can be used to force the module to use [ctypes][3] to reinterpret-cast the bits of the value as stored, instead of encoding it portably using the [struct][4] module. On almost all platforms, this will give the same results; on platforms that don’t natively use [IEEE floats][5], or store them in a different byte order than the primary byte order, this will instead give the _wrong_ results (but that may be useful to check for while experimenting).

[3]: https://docs.python.org/3/library/ctypes.html [4]: https://docs.python.org/3/library/struct.html [5]: http://en.wikipedia.org/wiki/IEEE_floating_point

## Differences from Decimal

A fixed-size binary float is of course not identical to an arbitrary-size decimal float. That means the tuple representation is significantly different. In particular:

Decimal is stored as an integer plus an exponent, with separate special exponents for infinity, quiet NaN, and signaling NaN (F, n, and N, respectively).

float is stored as a fraction between 1 and 2, with the leading 1 implicit, plus an exponent, with a single special exponent for infinity and both NaNs (1024, which is infinity if all digits are 0, otherwise NaN, quiet if the first digit is 1) and another one for zero and denormal values (-1023, which is treated as -1022 but without the implicit leading 1 on the fraction).

The differences are easier to see through experimentation than explanation (which is partly why this module exists).

## Motivation

Python’s Decimal type represents an IEEE 854-1987 decimal float, and it comes with a number of handy operations for exploring the details of that representation, like the [next_plus][6] family and [as_tuple][6]. And sometimes these operations are useful beyond exploration—e.g., to test whether the result of an algorithm is within 1 ulp of the expected result.

[6]: https://docs.python.org/3/library/decimal.html#decimal.Decimal.next_plus [7]: https://docs.python.org/3/library/decimal.html#decimal.Decimal.as_tuple

However, while the built-in float type nearly always represents an IEEE 754-1985 binary float, for which the same operations would be handy, they aren’t included.

Of course it’s possible to get the bits of a float and operator on them manually, as explained in [IEEE Floats and Python][8], it isn’t nearly as convenient.

[8]: http://stupidpythonideas.blogspot.com/2015/01/ieee-floats-and-python.html

So, this module provides similar functions for float.

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