Math functions ¶

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https://martinheinz.dev ¶

Meanwhile in the math module, bunch of miscellaneous functions were added or improved. Starting with the improvement to one existing function:

math.gcd ¶

             import math

# Greatest common divisor
math.gcd(80, 64, 152)
# 8

Previously gcd function which calculates the Greatest Common Divisor could only be applied to 2 numbers, forcing programmers to do something like this math.gcd(80, math.gcd(64, 152)), when working with more numbers.

Starting with Python 3.9, we can apply it to any number of values.

math.lcm ¶

math.lcm calculates Least Common Multiple of its arguments. Same as with GCD, it allows variable number of arguments.

First new addition to math module is math.lcm function:

             # Least common multiple
math.lcm(4, 8, 5)
# 40

            

math.nextafter ¶

The 2 remaining new functions are very much related.

These are math.nextafter and math.ulp :

             # Next float after 4 going towards 5
math.nextafter(4, 5)
4.000000000000001
# Next float after 9 going towards 0
math.nextafter(9, 0)
8.999999999999998

            

The math.nextafter(x, y) function is pretty straightforward - it’s next float after x going towards y while taking into consideration floating-point number precision.

math.ulp (Unit in the Last Place) ¶

The math.ulp on the other hand might look little weird…

ULP stands for “Unit in the Last Place” and it’s used as a measure of accuracy in numeric calculations. Shortest explanation is using an example:

Let’s imagine that we don’t have 64 bit computer. Instead, all we have is just 3 digits. With these 3 digits we can represent number like 3.14, but not 3.141.

With 3.14, the nearest larger number that we can represent is 3.15,

These 2 numbers differ by 1 ULP (Units at the last place), which is 0.1.

So, what the math.ulp returns is equivalent of this example, but with actual precision of your computer.

             # Unit in the Last Place
math.ulp(1000000000000000)
0.125

math.ulp(3.14159265)
4.440892098500626e-16

            

For proper example and explanation see nice writeup at https://matthew-brett.github.io/teaching/floating_error.html .