pychop 0.0.5

Python code for simulating low precision floating-point arithmetic

pychop

A python package for simulaing low precision floating point arithmetic in scientific computing

Using low precesion can gain extra speedup while resulting in less storage and energy cost. The intention of pychop, following the same function of chop in Matlab provided by Nick higham, is to simulate the low precision formats based on single and double precisions, which is pravalent on modern machine.

The supported rounding modes include:

1. Round to nearest using round to even last bit to break ties (the default).

2. Round towards plus infinity (round up).

3. Round towards minus infinity (round down).

4. Round towards zero.

5. Stochastic rounding - round to the next larger or next smaller floating-point number with probability proportional to the distance to those floating-point numbers.

6. Stochastic rounding - round to the next larger or next smaller floating-point number with equal probability.

Subnormal numbers is supported, they are flushed to zero if it not considered (by setting subnormal to 0).

The supported floating point arithmetic formats include:

format	description
'q43', 'fp8-e4m3'	NVIDIA quarter precision (4 exponent bits, 3 significand (mantissa) bits)
'q52', 'fp8-e5m2'	NVIDIA quarter precision (5 exponent bits, 2 significand bits)
'b', 'bfloat16'	bfloat16
'h', 'half', 'fp16'	IEEE half precision (the default)
's', 'single', 'fp32'	IEEE single precision
'd', 'double', 'fp64'	IEEE double precision
'c', 'custom'	custom format

This package provides consistent APIs to the chop software by Nick higham as much as possible. For the first four rounding mode, with the same user-specific parameters, pychop generates exactly same result as that of the chop software. For stochastic rounding (rmode as 5 and 6), both output same results if random numbers is given the same.

Install

pychop has the only following dependency:

• numpy >=1.7.3

To install the current pychop release via PIP use:

pip install pychop

To check the pychop installation use:

python -m pip show pychop

Usage

After installing pychop, load the pacakge by import pychop (of course you can use from pychop import chop for saving a lot code).

We use an simple example to illustrate its usage:

x = np.array([0.07630829, 0.77991879, 0.43840923, 0.72346518, 0.97798951]); 

cp = pychop.chop(prec='h', rmode=3) # use chop(prec='h', rmode=3) if you load with from pychop import chop
c = cp.chop(x)
print(c)

Output [0.07629395 0.77978516 0.43823242 0.72314453 0.97753906].

References

[1] Nicholas J. Higham and Srikara Pranesh, Simulating Low Precision Floating-Point Arithmetic, SIAM J. Sci. Comput., 2019.

[2] IEEE Standard for Floating-Point Arithmetic, IEEE Std 754-2019 (revision of IEEE Std 754-2008), IEEE, 2019.

[3] Intel Corporation, BFLOAT16---hardware numerics definition, 2018