Comparison

Comparison matrix

Fixed-point libraries

Library	APyTypes	en_cl_fix	fixedpoint	fpbinary	fxpmath	numfi	pychop	pyfixp	spfpm
Custom fixed-point formats	Yes	Yes	Yes	Yes	Yes	Yes [2]	Yes	Yes	Yes
Custom floating-point formats	Yes	No	No	No	No	No	Yes	No	No
Maximum wordlength [6]	None	53/None [1]	None	None	None	64 [2]	53 [3]	53 [4]	None
Resizing of fixed-point results	Yes	Yes	Yes	Yes	Yes	Yes [2]	Yes [3]	Yes [4]	No
Arrays	Yes	Yes	No	No [5]	Yes	Yes	Yes [3]	Yes [4]	No
Matrix multiplication (@)	Yes	No	N/A	N/A	No	No	Yes [3]	Yes [4]	N/A
Written in	C++/Python	Python	Python	C/Python	Python	Python	Python [3]	Python [4]	Python

Footnotes

[1]

en_cl_fix has two different fixed-point classes, one handles up to 53 bits, the other has no limitation. However, an operation involving the shorter format cannot produce the longer etc. In the comparison, the longer format was used for all tests.

[2] (1,2,3)

numfi is limited to 64 total bits (including results of e.g. multiplication).

[3] (1,2,3,4,5)

pychop is essentially a package to simply quantize floating-point NumPy, PyTorch, and JAX-arrays to a corresponding fixed-point or floating-point representation. Computation still happens at the precision of the underlying array.

[4] (1,2,3,4,5)

pyfixp is essentially a package to simply quantize floating-point NumPy-arrays with doubles to a corresponding fixed-point representation. Computation still happens at the precision of the underlying array.

[5]

fpbinary provides a helper function to convert an array to a list with fixed-point numbers.

[6]

Note that this holds for intermediate results as well. For example, multiplying two 27-bit numbers will create a 54-bit result which will not give bit-accurate results with pyfixp.

Floating-point libraries

Library	APyTypes	bigfloat [7]	gmpy2 [8]	mpmath	PyChop	PyMPF	gfloat
Custom fixed-point formats	Yes	No	No	No	Yes [9]	No	No
Custom floating-point formats	Yes	Yes	Yes	Yes	Yes [9]	Yes	Yes [10]
Binary representation of number [11]	Yes	No	No	No	No	Yes	Yes
Maximum wordlength	32 bits for exponent, 64 bits for mantissa [12]	None	None	None	Yes [9]	18 bits for exponent, none for mantissa	Yes [10]
Stochastic rounding	Yes	No	No	No	Yes	No	Yes [10]
Arrays	Yes	No	No	Yes	Yes [9]	No	Yes [10]
Matrix multiplication (@)	Yes	N/A	N/A	Yes	Yes [9]	N/A	Yes [10]
Written in	C++/Python	C/Python	C/Python	Python [13]	Python [9]	Python	Python [10]

Footnotes

[7]

bigfloat is a Python wrapper around the GNU MPFR library.

[8]

gmpy2 is a Python wrapper around the GNU MPFR and GNU MPC libraries.

[9] (1,2,3,4,5,6)

pychop is essentially a package to simply quantize floating-point NumPy, PyTorch, and JAX-arrays to a given fixed-point or floating-point representation. Computation still happens at the precision of the underlying array.

[10] (1,2,3,4,5,6)

gfloat is a package for encoding/decoding floating-point numbers. Floating-point NumPy, PyTorch, and JAX-arrays are quantized to a given floating-point representation, and computation still happens at the precision of the underlying array.

[11]

This means that it is possible to get a binary representation for comparison with, e.g., a hardware implementation.

[12]

This is a design choice since apytypes is aimed at simulating shorter custom formats. However, there is unlimited word length support for fixed-point values which can, if deemed suitable at a later time, be used for floating-point as well.

[13]

mpmath can use gmpy as a backend to do faster arithmetic, but uses Python integers by default.

Performance Comparison

This benchmark compares relevant fixed-point libraries from the list above. It is updated every documentation build and may vary over time as the code is further optimized.

Feature Comparison