PRECISE

Precision Rules Enforced Calculations In Scientific Environments

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About The Project

FIXME

Getting Started

FIXME

Available modules

sig_float »

This module provides the infrastructure to preform calculations that behave according to significant figure rules. An instance of the sig_float class may be added, subtracted, multiplied, or divided with another sig_float using standard operators. The resultant will retain the proper number of significant figures. Units can optionally be provided.

sig_const »

This module provides several commonly used constants of type sig_float.

sig_float

About The Module

This module provides the infrastructure to preform calculations that behave according to significant figure rules. An instance of the sig_float class may be added, subtracted, multiplied, or divided with another sig_float using standard operators. The resultant will retain the proper number of significant figures. Units can optionally be provided.

Getting Started

Import the sig_float class and round_sig function to your workspace

from sig_float import sig_float
from sig_float import round_sig

Usage

Usage table of contents

sig_float()
.sig_figs()
.precision()
.latex()
.exact()
Multiplication (*)
Exponential (**)
Division (/)
Addition (+)
Subtraction (-)
str()
bool()
float()
round_sig()

sig_float()

sig_float(str_num:str="0", units:dict=dict(), exact:bool=False) -> None:

A sig_float object is designed to be used in situations in which the user wants to preform calculations which retain the proper significant figures and units. the recommended usage of a sig_float object is is to create variables of type sig_float then use those variables in a mathematical expressions.

str_num="0": A string argument containing a numeric value. Scientific notation may also be used with standard python scientific formatting.

R = sig_float("0.08206")
C = sig_float("3.00e+8", {"m":1, "s":-1})

units=dict(): A dictionary of units in which the key is a string representation of the unit, and the value is the power to which it is raised. Negative exponents may be used.

R = sig_float("0.08206", {"L":1, "atm":1, "mol":-1, "K":-1})

exact=False: A boolean describing if a number is exact. If exact is set to True, this sig_float will not affect the rounding of operations.

R = sig_float("0.08206", {"L":1, "atm":1, "mol":-1, "K":-1}, exact=True)

Usage example

V1 = sig_float("2.00", {"L":1})
P1 = sig_float("752.0", {"mmHg":1})
T1 = sig_float("293", {"K":1})
P2 = sig_float("2943", {"mmHg":1})
T2 = sig_float("273", {"K":1})
V2 = (T2 * P1 * V1) / (P2 * T1)
# V2 has value of sig_float("0.476", {"L", 1})

.sig_figs()

.sig_figs()->int:

Returns the number of significant digits for a given sig_float object. Sig figs are calculated using the following sig fig rules:

All non-zero digits are significant.
All captive zeros are significant.
Trailing zeros are only significant if they follow a decimal point
Leading zeros are never significant.

num = sig_float("0012000.")
num.sig_figs()
# Results in 5

.precision()

.precision() -> int:

Returns the number of places to which the number is precise to. A negative number is returned if the number is precise to a whole number.

What does the precision value mean? Given the number 1234.567, the following precisions are assigned to each digit.


Number	1	2	3	4	.	5	6	7
Precision	-3	-2	-1	0		1	2	3

a = sig_float("200")
a.precision()
# Results in -2

b = sig_float("200.")
b.precision()
# Results in 0

c = sig_float("0.0020")
c.precision()
# Results in 4

.latex()

.latex(format:int=1, sci:bool=False)->str:

Formats sig_float to a $\LaTeX{}$ string. An argument may be provided to choose a unit format type. An additional argument may be used to change the number format to scientific.

The following sig_float is used in subsequent examples:

R = sig_float("0.08206", {"L":1, "atm":1, "mol":-1, "K":-1}, exact=True)

format=1: (default): Units represented on one line using negative exponents

print(R.latex(format=1))  # Or print(R.latex())
# Outputs: 0.08206 \; L \cdot atm \cdot mol^{-1} \cdot K^{-1}

$\large 0.08206 ; L \cdot atm \cdot mol^{-1} \cdot K^{-1}$

format=2: Units represented as a fraction

print(R.latex(format=2))
# Outputs: 0.08206 \frac{L \cdot atm}{mol \cdot K}

$\large 0.08206 \frac{L \cdot atm}{mol \cdot K}$

format=3: Units represented on one line using a fraction

print(R.latex(format=3))
# Outputs: 0.08206 \; L \cdot atm / mol \cdot K

$\large 0.08206 ; L \cdot atm / mol \cdot K$

- - -

The following sig_float is used in subsequent examples:

C = sig_float("3.00e+8", {"m":1, "s":-1})

sci=False (default): Number represented in standard format

print(C.latex(sci=False))
# Outputs: 30\bar{0}000000 \; m \cdot s^{-1}

$\large 30\bar{0}000000 ; m \cdot s^{-1}$

sci=True (default): Number represented in standard format

print(C.latex(sci=True))
# Outputs: 3.00 \times 10^{8} \; m \cdot s^{-1}

$\large 3.00 \times 10^{8} ; m \cdot s^{-1}$

.exact()

.exact() -> bool

Returns if a given sig_float is exact or not.

a = sig_float("1", exact=True)
b = sig_float("3", exact=True)
c = a / b
print(f"{a} / {b} = {c}. Exact? {c.exact()}")
# Outputs: 1 / 3 = 0.3333333333333333. Exact? True

Multiplication (*)

sig_float * sig_float

Multiplies two operands of type sig_float using the standard multiplication operator (*). The resulting product is a number of type sig_float rounded to the proper number of sig figs according to the following sig fig rule:

In multiplication and division, the result should be rounded to the least number of significant figures of any one term.