Significantdigits

Solid statistical analysis of Stochastic Arithmetic.

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README

significantdigits package - v0.4.0

Compute the number of significant digits based on the paper Confidence Intervals for Stochastic Arithmetic. This package is also inspired by the Jupyter Notebook included with the publication.

Getting started
Installation
Advanced Usage
Recent Improvements
Testing
License

Getting started

This synthetic example illustrates how to compute significant digits of a results sample with a given known reference:

>>> import significantdigits as sd
>>> import numpy as np
>>> from numpy.random import uniform as U
>>> np.random.seed(0)
>>> eps = 2**-52
>>> # simulates results with epsilon differences
>>> X = [1+U(-1,1)*eps for _ in range(10)]
>>> sd.significant_digits(X, reference=1)
>>> 51.02329058847853

or with the CLI interface assuming X is in test.txt:

> significantdigits --metric significant -i "$(cat test.txt)" --input-format stdin --reference 1
> (51.02329058847853,)

If the reference is unknown, one can use the sample average:

...
>>> sd.significant_digits(X, reference=np.mean(X))
>>> 51.02329058847853

To print the result as mean +/- error, use the format_uncertainty function:

>>> print(sd.format_uncertainty(X, reference=1))
>>> ['+1.00000000000000000 ± 1.119313369151395181e-16'
     '+1.00000000000000000 ± 1.119313369151395181e-16'
     '+1.00000000000000000 ± 1.119313369151395181e-16'
     '+1.00000000000000000 ± 1.119313369151395181e-16'
     '+1.00000000000000000 ± 1.119313369151395181e-16'
     '+1.00000000000000000 ± 1.119313369151395181e-16'
     '+1.00000000000000000 ± 1.119313369151395181e-16'
     '+1.00000000000000022 ± 1.119313369151395181e-16'
     '+1.00000000000000022 ± 1.119313369151395181e-16'
     '+1.00000000000000000 ± 1.119313369151395181e-16']

Installation

python3 -m pip install -U significantdigits

or if you want the latest version of the code, you can install it from the repository directly

python3 -m pip install -U git+https://github.com/verificarlo/significantdigits.git
# or if you don't have 'git' installed
python3 -m pip install -U https://github.com/verificarlo/significantdigits/zipball/master

Examples

The examples directory contains several example scripts demonstrating how to use the significantdigits package in different scenarios. You can find practical usage patterns, sample data, and step-by-step guides to help you get started or deepen your understanding of the package's features.

Advanced Usage

Inputs types

Functions accept the following types of inputs:

    InputType: ArrayLike

Those types are accessible with the numpy.typing.ArrayLike type.

Z computation

Metrics are computed using Z, the distance between the samples and the reference. There are four possible cases depending on the distance and the nature of the reference that are summarized in this table:

| | constant reference (x) | random variable reference (Y) | | ------------------ | ---------------------- | ----------------------------- | | Absolute precision | Z = X - x | Z = X - Y | | Relative precision | Z = X/x - 1 | Z = X/Y - 1 |

_compute_z(array: InternalArrayType, 
           reference: InternalArrayType | None, 
           error: Error | str, 
           axis: int, 
           shuffle_samples: bool = False) -> InternalArrayType
    Compute Z, the distance between the random variable and the reference

    Compute Z, the distance between the random variable and the reference
    with three cases depending on the dimensions of array and reference:

    X = array
    Y = reference

    Three cases:
    - Y is none
        - The case when X = Y
        - We split X in two and set one group to X and the other to Y
    - X.ndim == Y.ndim
        X and Y have the same dimension
        It it the case when Y is a random variable
    - X.ndim - 1 == Y.ndim or Y.ndim == 0
        Y is a scalar value

    Parameters
    ----------
    array : InternalArrayType
        The random variable
    reference : InternalArrayType | None
        The reference to compare against
    error : Error | str
        The error function to use to compute error between array and reference.
    axis : int, default=0
        The axis or axes along which compute Z
    shuflle_samples : bool, default=False
        If True, shuffles the groups when the reference is None

    Returns
    -------
    array : InternalArrayType
        The result of Z following the error method choose
    scaling_factor : InternalArrayType
        The scaling factor to compute the significant digits
        Useful for absolute error to normalizing the number of significant digits
        ``When Y is a random variable, we choose e = ⎣log_2|E[Y]|⎦+1.``p.10:9

Methods

Two methods exist for computing both significant and contributing digits depending on whether the sample follows a Centered Normal distribution or not. You can pass the method to the function by using the Method enum provided by the package. The functions also accept the name as a string "cnh" for Method.CNH and "general" for Method.General.

class Method(AutoName):
    """
    CNH: Centered Normality Hypothesis
         X follows a Gaussian law centered around the reference or
         Z follows a Gaussian law centered around 0
    General: No assumption about the distribution of X or Z
    """
    CNH = auto()
    General = auto()