README

Basic utility functions for converting between strings and np.float128 floating point numbers.

np.float128's are actually C-style longdoubles in an 80-bit format, not full quad-precision,
(see http://en.wikipedia.org/wiki/Extended_precision) but are stored in 128 bits of memory.

Python's native methods for converting between strings and floating point numbers do
not work for np.float128's because the numbers get converted to np.float64's in the process.

Example:
import numpy as np
np.longdouble(0.1234567890123456789)

produces an output of
0.12345678901234567737

The last few digits are lost here because the string of numbers is first converted
to a double (np.float64), which can only store ~15 significant decimal digits.

To avoid this issue, this package uses the arbitrary floating point precision mpmath
http://code.google.com/p/mpmath/
to convert the string and turn it into the correct longdouble number:

import longdouble_utils.py as ld
ld.string2longdouble('0.1234567890123456789')

produces an output of
0.1234567890123456789

Here, ~19 decimal digits of precision are accurately retained as a longdouble.

This package uses an intermediary format of a 'doubledouble', which is a tuple of 2
doubles where the first double has the same value as the result of simply casting the input string
to a double, and the 2nd double contains a correction factor such that upconverting both of the
doubles to longdoubles and adding them together yields the correct longdouble value.

This technique is based on algorithm from
http://web.mit.edu/tabbott/Public/quaddouble-debian/qd-2.3.4-old/docs/qd.pdf

Functions included interconvert between strings, doubledoubles, and longdoubles:
string2doubledouble
doubledouble2string
doubledouble2longdouble
longdouble2doubledouble
string2longdouble
longdouble2string