Golang floating point precision float32 vs float64

I wrote a program to demonstrate floating point error in Go:

func main() {
	a := float64(0.2) 
	a += 0.1
	a -= 0.3
	var i int
	for i = 0; a < 1.0; i++ {
		a += a
	}
	fmt.Printf("After %d iterations, a = %e\n", i, a)
}

It prints:

After 54 iterations, a = 1.000000e+00

This matches the behaviour of the same program written in C (using the double type)

However, if float32 is used instead, the program gets stuck in an infinite loop! If you modify the C program to use a float instead of a double, it prints

After 27 iterations, a = 1.600000e+00

Why doesn't the Go program have the same output as the C program when using float32?

Using math.Float32bits and math.Float64bits, you can see how Go represents the different decimal values as a IEEE 754 binary value:

Playground: https://play.golang.org/p/ZqzdCZLfvC

Result:

float32(0.1): 00111101110011001100110011001101
float32(0.2): 00111110010011001100110011001101
float32(0.3): 00111110100110011001100110011010
float64(0.1): 0011111110111001100110011001100110011001100110011001100110011010
float64(0.2): 0011111111001001100110011001100110011001100110011001100110011010
float64(0.3): 0011111111010011001100110011001100110011001100110011001100110011

If you convert these binary representation to decimal values and do your loop, you can see that for float32, the initial value of a will be:

0.20000000298023224
+ 0.10000000149011612
- 0.30000001192092896
= -7.4505806e-9

a negative value that can never never sum up to 1.

So, why does C behave different?

If you look at the binary pattern (and know slightly about how to represent binary values), you can see that Go rounds the last bit while I assume C just crops it instead.

So, in a sense, while neither Go nor C can represent 0.1 exactly in a float, Go uses the value closest to 0.1:

Go:   00111101110011001100110011001101 => 0.10000000149011612
C(?): 00111101110011001100110011001100 => 0.09999999403953552

Edit:

I posted a question about how C handles float constants, and from the answer it seems that any implementation of the C standard is allowed to do either. The implementation you tried it with just did it differently than Go.

Agree with ANisus, go is doing the right thing. Concerning C, I'm not convinced by his guess.

The C standard does not dictate, but most implementations of libc will convert the decimal representation to nearest float (at least to comply with IEEE-754 2008 or ISO 10967), so I don't think this is the most probable explanation.

There are several reasons why the C program behavior might differ... Especially, some intermediate computations might be performed with excess precision (double or long double).

The most probable thing I can think of, is if ever you wrote 0.1 instead of 0.1f in C.<br>
In which case, you might have cause excess precision in initialization<br>
(you sum float a+double 0.1 => the float is converted to double, then result is converted back to float)

If I emulate these operations

float32(float32(float32(0.2) + float64(0.1)) - float64(0.3))

Then I find something near 1.1920929e-8f

After 27 iterations, this sums to 1.6f