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A numeric type for Python storing floats in log space for increased precision, allowing positive and negative float computations (arithmetic and logical operations)

Project description

Class PyLogFloat

The PyLogFloat class transforms any float (positive or negative) in linear space into log_space and allows standard arithetic and logical operations in in linear space to be performed between two PyLogFloats.

Internally a float f is stored as follows:

  • the (natural) log of |f| is stored as in a numpy.float64 variable, p
  • the sign of f (‘-‘, ‘+’ or ‘0’) are stored in a variable (-1, +1, 0) variable, sign

By storing the sign separately, both positive and negative floats can be stored in a pyLogFloat. Notice that a sign=0 corresponds to the case where f =0.

Arithmetic operators

The following arithmetic operators are implemented:

+=
-=
*=
/=
+
-
*
/

Multiplication and division in linear space simply becomes addition and subtraction in log space. To implement linear space addition, the standard approach applying the log1p function is used. A conditional use of log1p or exp1m is used for log value subtractions, following Mächler, M. Accurately Computing log(1 − exp(− |a|)) Assessed by the Rmpfr package Cran, The Comprehensive R Archive Network.

The internal sign variable is taken into account when performing arithmetic operations. For example, in a multiplication between PyLogFloats a and b, corresponding to a positive float and a negative float, respectively, the resulting PyLogFloat has:

result.p = a.p + b.p
result.sign = a.sign * b.sign

Other operators are treated correspondingly (addition and subtraction becomes somewhat more involved).

Logical operators

The following arithmetic operators are implemented:

<=
>=
<
>

In logical operations between PyLogfloats a and b, the internal sign variable is first compared (-1 < 0 < +1).

If the a.sign == b.sign:

  • a.sign == 0 <=> equality
  • a.sign > 0, return a.p [operator] b.p
  • a.sing <0, return !(a.p [operator] b.p)

Other functions

Power operators (lplf**p, where plf is a pylogfloat and p is a float or int) are implemented:

**= (equiv ipow(self, p))
** (equiv pow(self, p))

Logarithms and exponents of PyLogFloat are implemented, both as inplace (e.g., ilog) and standard that is returning the result of the operation (e.g., log):

ilog(self)
log(self
iexp(self)
exp(self)

All functions and operators, except the power operator, are implemented to only work with PyLogFloats. The power operator always has a PyLogFloat base variable and a float or int power variable.

PLEASE NOTE THAT THIS IS STILL WORK IN PROGRESS

While a rudimentary test file is included, the class is still largely untested. Further functions may or may not be implemeted, e.g., a factorial function may be of interest. As could, in certain instances, automatic conversion of arguments to PyLogFloats.

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