how floats are printed

computers lie when they print out floats

(by rounding)

For example 0.12 isn’t 0.12, it’s actually (roughly):

0.119999999999999995559

is my computer LYING to me??? about NUMBERS?

the string -> float translation

If your program says:

x = 0.12

your interpreter / compiler needs to translate “0.12” into the float 0.119999999999999995559. Most languages will use the strtod (“string to double”) function from libc to do that translation.

the float -> string translation

This is where the rounding comes in. Computers round to make the numbers shorter and easier to read. 1.19999999999999995559

↪  1.2

float -> string translation is actually super complicated

Every floating point number needs a unique string representation.

There are a bunch of academic papers about how to do this well, search “Printing floating point numbers accurately” to read more about it.

some examples of printing floats

1.19900000000000006573

↪1.199

1.19999999000000001637

↪1.19999999

1.19999999999998996358

↪ 1.9999999999999

1.19999999999999995559

↪1.2

you can also print floats in base 16 or base 2

For example, 0.1 as a 32-bit float is:

base 16: 0x1.99999ap-4 (p-4 is the base 16. version of e-4)

base 2: 1.10011001100110011001101p-100

The base 2/base 16 representations are not rounded, but they’re rarely used.