Introduction

PMath is meant to be a library that resolves the inaccuracies of normal float math. PMath does not use any floats, and retains the most accurate format of a given number.

Remember:

• PMath is focused on accuracy, not speed or size
• All numbers must be converted to PNum before they are used, and all PNum numbers are accurate
• Currently, to do certain actions, like add radicals, you will have to convert to float. You will loose accuracy becuase you are using float math.

Module Division

• PMath (Main Module): Imports and exports basic and types
• Basic: Basic math ops, eg. add, subtract, multiply, divide...
• Types: Automatically imported, holds the PNum type and it's utils, eg. simplify, copyToRef, newPNum, $
• Expanded (Coming Soon): Other math functions like log, cos, sin, tan, etc.
• Constants: Contains math constants like i and PI.

Support

Feature	Radical Support	Fraction Support	Future Support	Notes
Radicals	✅ (All)
Fractions	✅ (All)
Additive Groups			✅	Goes with irrational numbers and adds support for adding and subtracting radicals.
Irrational Numbers			✅	E, PI, etc.
BigInt Support	✅ (All)
Imaginary Numbers	✅ (All)
Addition		✅
Subtraction		✅
Multiplication	✅	✅
Division	✅	✅
Exponents	✅	✅
Roots	✅	✅
Equals Operator	✅	✅
Comparison Operators	✅	✅
Shortcuts	✅	✅	✅	+=, *=, inc, etc.

Examples

Examples of the PMath library.

Basic Example

import pmath

## `!!` means that all math inside of the parentheses is PMath

echo !!(((1 / 3) + (5 / 4)) / 2 == (1 / 24) + (18 / 24))

echo !!(sqrt(5) * sqrt(3) == sqrt(15))

echo !!((1 / 4) * 3 - 5)

BigInt Examples (Calculating PI)

Please enable the -d:pmathBigInts flag to use bigints.

import pmath

## Leibniz’s formula

var pi = !0
var k = !1

for i in !!(0..(10 ^ 3)):
  
  if i mod 2 == 0:
    pi += !!(4 / k)
  else:
    pi -= !!(4 / k)
  
  k += 2

echo pi

proc readableFloat(pn: PNum): BiggestFloat =
  return BiggestFloat(pn * (10 ^ 8)) / BiggestFloat(10 ^ 8)

echo readableFloat(pi * 8) # Circumference of a circle with a diameter of 8. Should ~= 25

Accuracy Example

import pmath

var meters = 0.0
for _ in 1..100000000:
  meters += 0.01

echo meters
echo meters == 1000000 # false


let change = newPNum(1, 100) # Declared as let for speed
var meters2 = !0

for _ in 1..100000000:
  meters2 += change

echo meters2
echo meters2 == !1000000 # true