Small Python math library

Question

I have been writing a math library with more options than the standard builtin one, partially to make my life easier in the future, and partially just for practice. Here is what I have so far in the main file (master/xtrmth/xm.py):

import typing as tp
import decimal as dc

_meganum = tp.Union[int, float, dc.Decimal, tp.SupportsInt, tp.SupportsFloat]
_num = tp.Union[int, float, dc.Decimal]
_micronum = tp.Union[int, float]
_decnum = tp.Union[float, dc.Decimal]

def _total_round(value: _num, precision: int = 10, decimal: bool = False) -> _num:
    """Rounds 'value' to the nearest 'precision' digits."""
    if isinstance(value, int):
        return value
    elif precision < 0:
        raise ValueError('Cannot cast a negative integer onto \'xm._total_round(precision)\'')
    elif decimal is True:
        if isinstance(value, dc.Decimal):
            return round(value, precision)
        elif not isinstance(value, dc.Decimal) and decimal is True:
            raise TypeError('Cannot cannot cast \'float\' onto \'xm._total_round(value)\' \
with opperand \'decimal\' as \'True\'.')
    elif decimal is False:
        if isinstance(value, float):
            return round(value, precision)
        elif not isinstance(value, float):
            raise TypeError('Cannot cast \'decimal\' onto \'xm._total_round(value)\' \
with opperand \'decimal\' as \'False\'.')
    
def summation(count: int, bottom_var: str, expression: str, precision: int = 10, \
decimal: bool = False) -> _num:
    '''Summation function. Example: 'summation(4, 'z=1', 'z+1')' would return 14.'''
    
    if precision < 0:
        raise ValueError('Cannot cast a negative integer onto \'xm.summation(precision)\'')
    var, value = bottom_var.split('=')
    var = var.strip()
    
    if decimal is True:
        value = dc.Decimal(eval(value))
    else:
        value = int(eval(value))

    res = 0
    for i in range(value, count+1):
        res += eval(expression.replace(var, str(i)))

    if decimal is True:
        return _total_round(value=res, precision=precision, decimal=True)
    return _total_round(res, precision=precision, decimal=False)

def sq(value: _num, precision: int = 10, decimal: bool = False, _print_unround: bool = False) -> _micronum:
    '''Returns 'value' raised to the 2nd power, with 'precision' decimal points.'''
    if isinstance(value, float) and decimal is True:
        raise TypeError('Cannot cannot cast \'float\' onto \'xm.cb\' \
with opperand \'decimal\' as \'True\'.')
    elif isinstance(value, dc.Decimal) and decimal is False:
        raise TypeError('Cannot cannot cast \'decimal\' onto \'xm.cb\' \
with opperand \'decimal\' as \'False\'.')
    elif isinstance(value, dc.Decimal) and decimal is True:
        if _print_unround is True:
            print(value*value)
        return _total_round(value*value, precision, decimal=True)
    if _print_unround is True:
        print(value*value)
    return _total_round(value*value, precision, decimal=False)

def sqrt(value: _meganum, precision: int = 10, decimal: bool = False, _print_unround: bool = False) -> _num:
    if decimal is True:
        x = dc.Decimal(value)
        y = dc.Decimal(1)
        e = dc.Decimal(0.000000000000000000000000000000000000000000000000000000000000000001)
    else:
        x = value
        y = 1
        e = 0.0000000000000000000000001
    
    while x - y > e:
        x = (x + y)/2
        y = value / x

    if _print_unround is True:
        print(x)

    return(_total_round(x, precision, decimal=decimal))

def cb(value: _meganum, precision: int = 10, decimal: bool = False, _print_unround: bool = False) -> _num:
    '''Returns 'value' raised to the 2nd power, with '''
    if isinstance(value, float) and decimal is True:
        raise TypeError('Cannot cannot cast \'float\' onto \'xm.cb\' \
with opperand \'decimal\' as \'True\'.')
    elif isinstance(value, dc.Decimal) and decimal is False:
        raise TypeError('Cannot cannot cast \'decimal\' onto \'xm.cb\' \
with opperand \'decimal\' as \'False\'.')
    elif isinstance(value, dc.Decimal) and decimal is True:
        if _print_unround is True:
            print(value*value*value)
        return _total_round(value*value*value, precision, decimal=True)
    if _print_unround is True:
        print(value*value*value)
    return _total_round(value*value*value, precision, decimal=False)

def cbrt(value, _print_unround: bool = False) -> _num:
    x = value**(1/3)

    if _print_unround is True:
        print(x)

    if type(x) is float:
        if round(x, 10) == int(round(x, 10)): return int(round(x, 10))
        return round(x, 10)
    return x

def xpn(base: _meganum, exponent: _meganum, decimal: bool = False, precision: int = 10, _print_debug: bool = False) \
-> _num:
    '''Raises 'base' to the power of 'exponent'.'''
    
    if not isinstance(base, dc.Decimal) and decimal is True:
        raise TypeError(f'Cannot cast \'{type(base).__name__()}\' onto \'xm.xpn(base)\' with opperand \'decimal\' as \'True\'')
    elif isinstance(base, dc.Decimal) and decimal is False:
        raise TypeError('Cannot cast \'decimal.Decimal\' onto \'xm.xpn(base)\' with opperand \'decimal\' as \'False\'')
        
    out = 1
    
    if isinstance(exponent, int):
        if _print_debug is True:
            print('exponent is int')
        for i in range(exponent):
            if _print_debug is True:
                print(out)
            out *= base
        return _total_round(out, precision=precision, decimal=decimal)
    else:
        # will update with my own algorithim in a later update
        return _total_round(base**exponent, precision=precision, decimal=decimal)

def rt(base: _meganum, root: _meganum, precision: int = 10, decimal: bool = False, _print_debug: bool = False) -> _num:
    '''Takes the 'root' root of 'base' '''

    if isinstance(base, dc.Decimal) and decimal is False:
        raise TypeError('Cannot cast \'decimal.Decimal\' onto \'xm.rd(base)\' with opperand \'decimal\' as \'False\'')
    elif not isinstance(base, dc.Decimal) and decimal is True:
        raise TypeError(f'Cannot cast \'{type(base).__name__}\' onto \'xm.rd(base)\' with opperand \'decimal\' as \'False\'')
    elif isinstance(root, dc.Decimal) and decimal is False:
        raise TypeError('Cannot cast \'decimal.Decimal\' onto \'xm.rd(root)\' with opperand \'decimal\' as \'False\'')
    elif not isinstance(root, dc.Decimal) and decimal is True:
        raise TypeError(f'Cannot cast \'{type(root).__name__}\' onto \'xm.rd(root)\' with opperand \'decimal\' as \'True\'')
    
    if decimal is True:
        return xpn(base = base, exponent = (dc.Decimal(1) / root), decimal = True, precision = precision, _print_debug = _print_debug)
    return xpn(base = base, exponent = (1 / root), decimal = False, precision = precision, _print_debug = _print_debug)

Is there anything I should change?

Github page: Github
PyPI page: PyPI

Answer 1

General

import typing as tp => from typing import Union reduces acronyms reader needs to remmber

Backslashes are scary. Adding parentheses or in this case trusting the existing ones will be easier to read.

def summation(count: int, bottom_var: str, expression: str, precision: int = 10, \
decimal: bool = False) -> _num:

Again, backslashes are scary.

raise ValueError('Cannot cast a negative integer onto \'xm.summation(precision)\'')
# could be
raise ValueError("Cannot cast a negative integer onto 'xm.summation(precision)'")

There are a lot of underscores here. Exposing the important functions in an separate file would reduce the need to hide everything.

Functions

Each of your functions are written in a pretty similar style, so I'll just look at one of them.

def rt(base: _meganum, root: _meganum, precision: int = 10, decimal: bool = False, _print_debug: bool = False) -> _num:
    '''Takes the 'root' root of 'base' '''

    if isinstance(base, dc.Decimal) and decimal is False:
        raise TypeError('Cannot cast \'decimal.Decimal\' onto \'xm.rd(base)\' with opperand \'decimal\' as \'False\'')
    elif not isinstance(base, dc.Decimal) and decimal is True:
        raise TypeError(f'Cannot cast \'{type(base).__name__}\' onto \'xm.rd(base)\' with opperand \'decimal\' as \'False\'')
    elif isinstance(root, dc.Decimal) and decimal is False:
        raise TypeError('Cannot cast \'decimal.Decimal\' onto \'xm.rd(root)\' with opperand \'decimal\' as \'False\'')
    elif not isinstance(root, dc.Decimal) and decimal is True:
        raise TypeError(f'Cannot cast \'{type(root).__name__}\' onto \'xm.rd(root)\' with opperand \'decimal\' as \'True\'')
    
    if decimal is True:
        return xpn(base = base, exponent = (dc.Decimal(1) / root), decimal = True, precision = precision, _print_debug = _print_debug)
    return xpn(base = base, exponent = (1 / root), decimal = False, precision = precision, _print_debug = _print_debug)

• You can afford more than 2 characters for a function name.
• The Decimal type as an edge case clutters up both your usage and your library code.
• The conditional statements can be removed by taking advantage of features these types already have

def nth_root(base: _meganum, n: _meganum, precision: int = 10) -> _num:
    '''Takes the nth root of 'base' '''
    # works for Decimals, ints, floats, whatever
    exponent = n ** -1
    return xpn(base=base, exponent=exponent, precision=precision)

Answer 2

What's going on here?

elif decimal is True:
    ⋮
elif decimal is False:

Firstly, especially since we annotated that decimal is boolean, we should just be testing its truthiness; secondly, at the elif we already know that decimal isn't true. So, simply write

elif decimal:
    ⋮
else:

Applying this simple change throughout already cuts a lot of unnecessary verbiage and improves the readability.

The immediately preceding code shows we shouldn't be in elif anyway

if isinstance(value, int):
    return …
elif precision < 0:
    raise …
elif decimal is True:

Since return and raise both exit the flow of control, we can reduce cognitive load thus:

if isinstance(value, int):
    return …
if precision < 0:
    raise …
if decimal:

Looking inside the if decimal case, we see:

  elif decimal is True:
        if isinstance(value, dc.Decimal):
            return …
        elif not isinstance(value, dc.Decimal) and decimal is True:
            raise …

In last condition, we know that decimal is true and that value is not a dc.Decimal, so that one just becomes a plain else - and not needed because the previous clause returned:

  elif decimal:
        if not isinstance(value, dc.Decimal):
            raise …
        return …

Just simplifying the control flow in that one function makes it a lot simpler:

def _total_round(value: _num, precision: int = 10, decimal: bool = False) -> _num:
    """Rounds 'value' to the nearest 'precision' digits."""
    if isinstance(value, int):
        return value
    if precision < 0:
        raise ValueError("Cannot cast a negative integer onto 'xm._total_round(precision)'")
    if decimal and not isinstance(value, dc.Decimal):
        raise TypeError("Cannot cannot cast 'float' onto 'xm._total_round(value)' \
with operand 'decimal' as 'True'.")
    if not decimal and not isinstance(value, float):
        raise TypeError("Cannot cast 'decimal' onto 'xm._total_round(value)' \
with operand 'decimal' as 'False'.")
    return round(value, precision)

---

Looking again from further away, I don't see any unit-tests at all. What happened to them?