Efficient operations on arrays of extremely large or small numbers.

Xrange_array is a numpy nd.array subclass which allows to represent floating-point numbers in an extended range:

• [1.e-646456992, 1.e+646456992].

Float or complex numbers in simple or double precision with an extra base-2 exponent stored as int32 are implemented.
It also provides real and complex implementation for:

• The main binary operations (+, -, *, /, <, <=, >, >=)
• a few selected complex functions (abs, angle, sqrt, square, conj, log)
• an abs2 function: optimal implementation of square of abs for complex numbers.

Their use is transparent to the user, as they follow numpy general API.

Basic use:

>>> Xa = Xrange_array([["123.456e-1789", "-.3e-7"], ["1.e700", "1.0"]])
>>> print(Xa**2)
[[ 1.52413839e-3574 9.00000000e-16]
 [ 1.00000000e+1400 1.00000000e+00]]

Accurate base-10 conversion for string-inputs and printing:

>>> Xb = np.array([1., -1.j]) * np.pi * Xrange_array(["1.e+646456991","1.e-646456991" ])
>>> with np.printoptions(precision=13) as _:
        print(Xb)
[ 3.1415926535898e+646456991➕0.0000000000000e+00j
  0.0000000000000e+00➖3.1415926535898e-646456991j]

Performance compared with standard np.complex128 operations on large (40'000) arrays:

• square overhead ratio: 12.6
• add overhead ratio: 10.6
• multiply overhead ratio: 4.3
• abs2 overhead ratio: 2.2

Xrange_polynomial represents a polynomial with extended range coefficients. It implements the basic operations +, -, *.

Xrange_SA is a subclass of Xrange_polynomial representing series approximations of a function. Compared to Xrange_polynomial it keeps track of a truncature error (high order terms ignored during multiplication).