pylogfloat 0.1.2

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

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

Multiplication and division in linear space simply becomes addition and subtraction in log space. To implement linear space addition and subtraction, the conditional use of log1p or exp1m for log value additions and subtractions, following Martin, 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

In logical operations (<,``>``,``<=``,``>=``) between PyLogfloats a and b, the internal sign variable is first checked (-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

The power operator (‘**’, ‘^’) are also implemented, as are self.pow and a self.log functions.

All functions and operators, except the power operator, are implemented to only work between two 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 i s included, the class is still largely untested. Further functions may or may not be implemeted, e.g., a factorial function may be of interest.